By Patricia Zengerle

WASHINGTON, Oct 14 (Reuters) - U.S. lawmakers urged President Barack Obama to keep to a hard line on sanctions imposed on Iran on Monday, a day before the resumption of talks on its nuclear program between world powers and Tehran.

Congress has generally been tougher on Iran than the Obama administration, pushing for ever-stricter economic measures over Tehran's nuclear program. On Monday, both Democrats and Republicans called for Obama to stand firm, even as an administration official held out the possibility of quick sanctions relief if Tehran moves quickly.

The talks starting in Geneva on Tuesday are the first since the June election of President Hassan Rouhani, a relative moderate who wants to thaw Iran's icy relations with the West to secure the removal of the punitive sanctions, which have hobbled its oil-based economy.

The House of Representatives overwhelmingly approved even stricter new sanctions in July. The Senate Banking Committee agreed to delay the package until after the Geneva negotiations only after appeals from the Obama administration.

In a letter to Obama, a group of six Democratic and four Republican U.S. senators said they were open to suspending the implementation of new sanctions on Iran but only if Tehran takes significant steps to slow its nuclear program.

The 10 senators said they wanted Tehran's full cooperation with the International Atomic Energy Agency, fulfillment of promises under the Nuclear Nonproliferation Treaty and implementation of all U.N. Security Council resolutions on its nuclear weapons program, including immediate suspension of all enrichment.

"If the Iranian government takes these steps in a verifiable and transparent manner, we are willing to match Iran's good-faith actions by suspending the implementation of the next round of sanctions currently under consideration by the Congress," they said.

'CREDIBLE MILITARY THREAT'

They also reaffirmed that "a credible military threat" remains on the table and said current sanctions must be maintained aggressively.

The 10 senators signing the letter included Democrats Robert Menendez, chairman of the Senate Foreign Relations Committee, and Charles Schumer, the No. 3 Democrat in the Senate, as well as Republicans John McCain and Lindsey Graham, two of their party's most influential foreign policy voices.

Other senior lawmakers took an even harder line.

The Republican chairman of the House Foreign Affairs Committee sent a separate letter urging Obama to negotiate "with the highest degree of caution." Washington should adopt new sanctions to gain additional leverage against Iran, Representative Ed Royce wrote.