In Switzerland, the U.S. is leading the push to conclude a deal with Iran that would halt Tehran’s nuclear program in exchange for a lifting of sanctions. But 3,000 miles away in Yemen, the U.S. is backing its ally Saudi Arabia in a bombing campaign targeting an Iranian proxy in the conflict that’s engulfing the Middle East. American policy is thus torn between a compromise with Iran and the support of Saudi Arabia, the Islamic Republic’s biggest rival.

But the conflicts in Yemen, Syria and Iraq are unlikely to affect the nuclear progam negotiations. In fact, experts said, the parties in Switzerland are going to ignore them altogether, in a difficult balancing act, as they attempt to patch together a tentative agreement in the last few days they have available -- and defer until later any discussion related to Iran’s expanding clout in the Middle East.

Iran and the so-called P5+1 group of world powers -- the U.S., Britain, China, France and Russia, plus Germany -- are racing to meet a March 31 deadline for a framework agreement. Both sides say they are committed to meeting this deadline for an initial agreement, and they have, so far, kept the nuclear talks separate from regional feuds.

“If the larger regional issues were included, for example, the Yemen conflict, it would bring an immediate halt to the progress of talks,” said Russell A. Berman, a senior fellow at the Hoover Institution, a public-policy think tank based at Stanford University in California. “The larger regional conflicts that are emerging between Iranian ambition and other interests are so profound that it requires a compartmentalization of the talks.”

Iran’s proxy Shiite militias now have strong footholds in Yemen, Syria and Iraq, as well as Lebanon. Their agendas sometimes are congruent with U.S. objectives, and sometimes are incongruent with them, complicating the picture.

In Yemen, the Iran-backed Houthi rebel group was able to seize the capital Sanaa last year. Despite Washington’s repeated warnings, the Houthis continued their advance in the country, effectively ousting a U.S.-backed president last month and eventually provoking an armed Saudi intervention.

This week, Saudi Arabia began airstrikes on targets in Yemen, in cooperation with other Arab and Gulf states, to defeat the Houthis and support the government of fugitive President Abdel Rabbo Mansour Hadi. The U.S. is cooperating by setting up a “joint planning cell in order to assist the Gulf Cooperation Council in communication, logistics and planning support,” a Defense Department official said via email. In other words, the proxy war in Yemen between Saudi Arabia and Iran is involving the U.S., as well.

In confusing contrast, Iranian forces in Iraq are indirectly helping the U.S. accomplish its main objective in the Middle East: the defeat of the Islamic State group, formerly known as either ISIL or ISIS.

Washington and Tehran may be fighting the same enemy, but both have been careful to avoid the appearance of direct cooperation.

In Iraq, Shiite militias backed by Iran now number in the hundreds of thousands and are the most powerful force battling the Islamic State group on the ground. This month, the militias led the first phase of an operation alongside the Iraqi army to eradicate the militant group in Tikrit, a Sunni city north of Baghdad. The U.S., which has refused to support any operations in Iraq that included Iranian proxies, has not hidden its concern over Iran’s influence in the region.

“We have concerns in a number of areas about Iran’s role,” State Department representative Jeff Rathke said at a press briefing Thursday while speaking of Iran’s influence in the region.

“Despite its tactical commonalities with Iran, Washington’s strategic goals in the region substantially differ from Tehran’s,” said Ali Vaez, the senior Iran analyst at the International Crisis Group, a nongovernmental organization based in Brussels. “Iran will fight ISIS because of the imperatives of its own national interest and regardless of the nuclear talks and relations with the U.S.”

Yet Iran’s growing influence in Iraq has not affected so far the nuclear negotiations. The two issues are likely to remain separate so long as “the Shiite militia behave themselves and don’t harm any American troops,” said Barbara Slavin, who focuses on the Iranian nuclear program as a nonresident senior fellow at the South Asia Center of the Atlantic Council, an international-affairs think tank headquartered in Washington.

However, Iran did try to use the fight against the Islamic State group as leverage in negotiations. In August, Iranian Foreign Minister Mohammad Javad Zarif told the country’s state media that Tehran would be willing to help the Sunnis and the U.S. fight the militant group in Iraq, if the U.S. agreed to lift “all the sanctions that are related to Iran’s nuclear program.” The American response was a swift, “No.”

“The U.S. basically said no dice, these are purely nuclear talks,” said James M. Acton, the co-director of the Nuclear Policy Program at the Carnegie Endowment for International Peace, a foreign-policy think tank based in Washington. “Iran didn’t push back very hard on this, I think because the Iranian negotiating team wants a deal and ... because they don’t want to derail it [with] broader security issues.”

Iran and the P5+1 group are now just days away from the deadline, making it unlikely either party will bring a new issue to the negotiating table. Next week’s deadline is basically meant to ensure the parties come to an agreement to later reach a deal. The details will then be further negotiated, with a June deadline for a comprehensive agreement.

But for all the effort the U.S. and Iran are making to separate the nuclear talks from the wider Middle East conflict, Iran’s growing role may become too large to ignore before the final deadline for a deal -- and it may give the Iranians an important bargaining chip.

“I think the [U.S.] administration wants to keep them separate,” the Hoover Institution’s Berman said. “It would be an extraordinary act of exclusion if they manage to keep them separate until June.”