As newly elected Iranian President Hasan Rouhani takes office, dozens of U.S. senators are urging the Obama administration to increase sanctions on the country -- to sustain pressure over Iran's nuclear program even as the U.S. tests the new diplomatic landscape.

Western diplomats are quietly hoping Rouhani's landslide election represents a turning point in Iran's relations with the West -- which were persistently sour under the leadership of Mahmoud Ahmadinejad. The economy has been crippled by international sanctions, and Rouhani has made clear his country would like to get out from under them, though he did not offer to end Iran's nuclear program.

Rouhani's inauguration was held Sunday. In a letter to President Obama released on Monday, 76 senators urged the administration to bring "a renewed sense of urgency" to the Iranian nuclear issue.

"We hope such a surprising and convincing electoral outcome will persuade Supreme Leader Ayatollah Ali Khamenei to abandon Iran's nuclear weapons quest," the senators wrote. "But until we see a significant slowdown of Iran's nuclear activities, we believe our nation must toughen sanctions and reinforce the credibility of our option to use military force at the same time as we fully explore a diplomatic solution to our dispute with Iran."

The senators noted that Rouhani has pledged to re-engage in multi-party talks regarding the nuclear program. They also noted that "Iran has used negotiations in the past to stall for time" and said it's important to "understand quickly" whether Tehran is serious this time.

They claimed the "toughening of sanctions" and the "convincing threat of the use of force" should help lead to a breakthrough.

During his inauguration -- the first since the 1979 revolution in which the government invited foreign dignitaries -- Rouhani warned against the use of sanctions.

"If you seek a suitable answer, speak to Iran through the language of respect, not through the language of sanctions," he said.

The White House noted Rouhani himself said his election represented a call by the Iranian people for change. "Should this new government choose to engage substantively and seriously to meet its international obligations and find a peaceful solution to this issue, it will find a willing partner in the United States," White House Press Secretary Jay Carney said.

Still, it's unclear that Rouhani can have any impact on Iran's nuclear program, which is controlled by the ayatollah. Experts say the U.S. needs to test that, quickly, but the question is how.

"One of the questions that the administration has to resolve is do you go big or do you go small?" said Jon Alterman, director of the Middle East Program for the Center for Strategic and International Studies. "You know, at what point do you try to fix everything and can you fix the small things if you don't change the whole context of the U.S. Iranian relationship?"

Fox News' Wendell Goler contributed to this report.