Senior American and Iranian officials spent over five hours together in private meetings in Geneva on Monday, jointly seeking a path forward in negotiations over Iran's nuclear program only six weeks before a self-imposed deadline on talks aimed at ending the crisis.

At the bilateral meeting, and in quotes placed in state-run Iranian media, Islamic Republic officials suggested world powers may have "no choice" but to extend the negotiations past the July 20 deadline. Talks have stalled over specific Western requests of Iran to dismantle key components of its vast nuclear infrastructure.

The US, United Kingdom, France, Russia, China and Germany agreed with Iran last fall to halt the crisis, and negotiate towards a comprehensive agreement to the longstanding impasse. International powers suspect Iran's nuclear program has military dimensions.

The interim deal reached last fall— formally known as the Joint Plan of Action— grants negotiators the ability to extend talks for six months after the July 20 deadline, should all parties consent.

"We hope to reach a final agreement (by July 20) but, if this doesn't happen, then we have no choice but to extend the Geneva deal for six more months while we continue negotiations," Deputy Foreign Minister Abbas Araqchi said, according to Iran's state-run news agency.

"It's still too early to judge whether an extension will be needed," Araqchi added. "This hope still exists that we will be able to reach a final agreement by the end of the six months on July 20."

EU officials sat in on parts of Monday's meeting between the US and Iran, which will continue Tuesday morning. The US and Iran only restarted bilateral relations in 2013 after decades of silence between the two governments, prompted by the Iranian Revolution in 1979.

"We've always said that we would engage the Iranians bilaterally," State Department deputy spokeswoman Marie Harf told reporters in Washington on Monday. No press conferences were scheduled in Geneva after the meetings. "We also said that there was going to be an intensification of diplomatic efforts."

Harf said that the US continues to work towards the July 20 deadline in the hopes of reaching a comprehensive plan of action.

In Herzelia, Israeli officials weighed in on the intensifying nuclear talks, with some suggesting the Iranians are seriously interested in a diplomatic solution and with others warning against a "bad deal" for the international community.

"We are worried about the negotiations, but we are also hopeful," Strategic Affairs Minister Yuval Steinitz told the 2014 Herzliya Conference on Monday.

An agreement that rids Iran of enriched uranium is obviously the best outcome, he said. But he is worried that the agreement that emerges would allow Iran to be a threshold nuclear state. “An international agreement that leaves Iran on the threshold of nuclear capability is worse than no agreement at all," Steinitz said.

"What is now at hand is not just the fate of Israel in the Middle East but the fate of the world," he said.

"When we speak to our allies, the Americans, we stress the main point is to prevent Iran from being on the threshold," he said.

If Iran is left on the threshold, he said, "Sooner or later Iran will reach nuclear capability, just like North Korea, which signed many agreements. Two or three years later, it broke through to nuclear weaponry. Today, we know it has 5-12 nuclear missiles."

A bad agreement would embolden other states to seek nuclear weapons without concern for sanctions, Steinitz said. "They will say, if it's possible for Iran to be considered legitimate and on the threshold of nuclear capability, why not give the same to Saudi Arabia, Egypt, Algeria, or Turkey?"

"When we look at the political negotiations, we are not against it, but we watch with concern," he said. "Always, we remind them that they need to ask themselves the same question – what will the Middle East look like in 10 years. The future is going to arrive, quicker than you think."

Another Israeli official said that the government of Prime Minister Benyamin Netanyahu is “concerned that the P5+1 is going to go and for a deal that allows Iran to freeze its program as a threshold nuclear state.”

“Freezing the Iranian nuclear program at a threshold level would be a historic mistake,” the official said.

With North Korea as an example of how negotiations can go awry the international community must ensure that all enriched uranium is removed from Iran.

“The international community must demand of Iran that it dismantle its military nuclear program, end all uranium enrichments, eliminate existing stock piles of of enriched uranium and end weaponization and it missile program,” the official said.

Iran can maintain a civilian nuclear program without any of these things, the Israeli official said.

Reuters contributed to this report.