The presidents of the United States and the United States' oldest ally, France, met today in Washington, and offered condolences to each other for recent violent tragedies suffered by each nation.

All of us are still grieving and in shock from the tragedy that took place, said President Barack Obama, referring to the shooting in Tucson, Arizona Saturday that took six lives and seriously wounded U.S. Rep. Gabrielle Giffords, D-AZ.

He and French President Nicholas Sarkozy had just emerged from a meeting at the White House.

Gabby Giffords and others are still fighting to recover, Obama said.  Families are still absorbing the enormity of their losses.

Obama called the shooting a heinous crime. The incident, the work of 22-year-old Tucson resident Jared Lee Loughner, now in custody, also injured 14 people, five of whom, including Giffords, remain in critical condition at University Medical Center in Tucson.

Obama also praised the heroism displayed at the Safeway mall, calling attention to the 20-year-old college student and Giffords' aide who tended her while awaiting professional help, as well as the three men and one woman who subdued the gunman.

The aide's name is Daniel Hernandez. Bill Badger, a retired Army colonel, and Roger Salzberger, who worked as a volunteer on Giffords' re-election campaign, tackled Loughner when he attempted to reload the 9-mm semi-automatic weapon after firing about 30 shots. Patricia Maisch and Joseph Zamudio joined them in holding the shooter down until authorities arrived.

Obama called these acts extraordinary courage...in the face of such mindless violence.

The President then reminded listeners that France just suffered a violent tragedy.

They just recently had two French citizens who were kidnapped in Niger.  It points to the challenge of terrorism that we jointly share, and this is just one more area in which cooperation between France and the United States is so critical, Obama said.

Antoine de Leocour, an aid worker in Niger, and his friend Vincent Delory, both 25, were kidnapped from a restaurant in Niamey at gunpoint Friday evening. Delory had recently arrived in Niger to attend de Leocour's wedding.

Islamic terrorists took the men and, apparently, executed them while fleeing Niger soldiers and French commandos, leaving their bodies in the desert.

Sarkozy called the kidnapping and murders a barbaric and cowardly act.

Both the U.S. and France are determined to stand firm as allies on this issue of terrorism, Sarkozy said.  Both of us believe that any show of weakness would be culpable.  We have no choice but to go after these terrorists wherever they may be.  When values as fundamental as those we cherish are being challenged, democracies cannot afford to give in.

The presidents said they discussed the G20 agenda and how they can address the many imbalances in the world economy that are inhibiting the prospects of growth, obama said.

France is the lead nation for the G20 in 2011 and will host the G20 summit this fall.

Although we are in the process of healing and recovery from the disastrous recession that we went through, we're not yet where we want to be, Obama said. Too many people are still out of work. Too many businesses are still having problems getting financing.

Sarkozy said he told Obama in very clear terms that we wish to work hand in glove, France and the United States, on these issues.

We are in the 21st century, and we need new ideas for this new century, Sarkozy said.

The leaders also discussed Afghanistan, Iran, the Middle East, the troubles in the Cote d'Ivoire and the election process in the Sudan.