Mitt Romney's immigration views are under scrutiny. Reuters

Mitt Romney will not modify the hard-line immigration stance he established during the Republican presidential primaries, the presumptive Republican nominee told supporters at a private meeting.

Politico reports that people at the meeting pushed Romney to counter President Barack Obama more aggressively on the issue. Obama recently bolstered his standing among Latinos, a demographic that overwhelmingly favors him over Romney, by announcing a new policy that will shield thousands of young immigrants from deportation and allow them to work legally.

You have to take the fight to Obama on this, NewsCorp CEO Rupert Murdoch reportedly told Romney.

Romney noted that he has enlisted the campaign trail help of Marco Rubio, an ascendant young Cuban-American senator from Florida, but added that I am not going to be a flip-flopper on immigration even if some of the positions he took during the primaries hurt him.

As Romney sought to rebuff criticism that he was too moderate to be the Republican standardbearer, he aligned himself with the strict pro-enforcement elements of the party. He took on Kansas Secretary of State Kris Kobach, the architect of the controversial Arizona immigration law, as an informal adviser; advocated a policy of encouraging self-deportation and denounced several reform measures, from the DREAM Act to offering in-state tuition to undocumented immigrants, as amnesty.

That appeared to serve him well in primaries dominated by more conservative voters, but his harsh rhetoric risks alienating moderates, not to speak of Latinos, in the general election. Romney has tread carefully, refusing to explicitly say he would repeal Obama's new policy and saying he would instead pursue comprehensive reform.

The contours of that reform emerged somewhat in a speech Romney delivered recently to the National Association of Latino Elected and Appointed Officials. Romney offered some ideas to streamline immigrant worker programs, offer more green cards to foreign students who get advanced degrees, and ease limits on green cards for immigrants' spouses and minor children of permanent residents.

Romney also stressed enforcing immigration laws, promising to fortify border security, tighten workplace enforcement and focus on measures to make legal immigration more attractive than illegal immigration. But he did not address what to do with the more than 11 million undocumented immigrants living in the United States.

I will address the problem of illegal immigration in a civil but resolute manner, Romney said. We may not always agree, but when I make a promise to you, I will keep it.