Iranians will have to decide whether they want to attend Fourth of July celebrations at U.S. embassies, President Obama said Tuesday, linking their attendance to the potential for warming between the two nations. 

The United States and Iran don't have formal diplomatic relations but Obama said that it's up to the Iranian diplomats to decide whether to use an invitation to attend embassy festivities as an opening.

"I think that we have said that if Iran chooses a path that abides by international norms and principles, then we are interested in healing some of the wounds of 30 years in terms of U.S.-Iranian relations. But that is a choice that the Iranians are going to have to make," Obama said during a press conference in the White House briefing room.

Despite a crackdown on protesters by the Iranian government, State Department spokesman Ian Kelley on Monday reaffirmed the invitation to Iranian diplomats to attend Independence Day parties at U.S. embassies around the world next month.

Kelly that no one is going to take back offers for Iranian officials to join the festivities, even as the Islamic Republic's leaders threaten violence against protesters at home demonstrating against falsified presidential election results.

"There's no thought to rescinding the invitations to Iranian diplomats," Kelly said. "We have made a strategic decision to engage on a number of fronts with Iran. And -- and we tried many years of isolation, and we're pursuing a different path now."

Late last month, the State Department encouraged officials at all U.S. embassies and consulates to ask their Iranian counterparts to attend the July 4 parties, which generally feature speeches about American values, fireworks, hot dogs and hamburgers.

The notice said that the posts "may invite representatives from the government of Iran" to the events.

The move came amid the administration's ongoing efforts to engage Iran in variety of venues, including formal diplomatic meetings over its nuclear program, violence in Iraq and the situation in Afghanistan.

But the decision "stunned" the ranking Republican on the House Foreign Affairs Committee

"I am stunned that some find it appropriate for U.S. officials to comingle with officials, representatives and agents of the Iranian regime this Independence Day. What kind of message does this send to the Iranian people, who are bravely standing up for the same rights and freedoms which Americans celebrate on this day?" asked Rep. Ileana Ros-Lehtinen, R-Fla., an outspoken critic of Iran, Cuba and other despotic regimes.

"It is time for the United States to rescind this invitation and, instead, express our unwavering support for the Iranian people and their dreams and ideals. This Independence Day, we must stand with all who yearn to live free, instead of fraternizing with their oppressors," she said.

It was not immediately clear how many embassies and consulates would actually invite Iranian diplomats to the July 4 parties or whether any Iranians would accept the invitations.