WASHINGTON -- U.S. Secretary of State Rex Tillerson said ties between Washington and Moscow were continuing to deteriorate, telling senators that the U.S. administration was still trying to stabilize the relationship.

Tillerson's June 13 comments to the Senate Foreign Relations Committee came one day after Congress moved closer to cementing existing sanctions on Moscow, and imposing new ones for Russia's alleged interference in last year's election, among other issues.

At a hearing on the State Department's new 2018 budget, senators grilled Tillerson on the department's priorities, not only Russia, but also China, North Korea, Syria, and other places.

Tillerson told senators that bilateral relations with Russia were at an all-time low. But he also ducked questions about whether he, or the White House, would support the new sanctions, or if the White House might try to veto it.

"We would like the flexibility to turn the heat up on Russia," he said. "We have some channels where we're starting to talk, but what I wouldn't want to do is close the channels off."

Russia Threatens Retaliatory Measures

President Donald Trump has voiced support for a more conciliatory approach to Russia, and immediately following his election, the Kremlin sent messages that suggested it was hoping for some sort of sanctions relief.

In recent weeks, however, as it became clear that the White House was not moving to lift existing ones, and as Congress moved to impose new ones, Moscow's tone has sharpened.

Last week, Russian officials threatened retaliatory measures, including seizing a U.S. Embassy property in western Moscow. That appeared targeted at the U.S. seizure of two Russian compounds in Maryland and New York, which U.S. law enforcement said had been used for intelligence gathering purposes.

Kremlin spokesman Dmitry Peskov said on June 13 that Moscow is "closely following" the new sanctions legislation. Asked about the bipartisan initiative, Peskov said the Kremlin's impression was "negative."

The new measures targeting Russia, agreed to by Republican and Democratic senators on June 12, were contained in an amendment to be attached to a pending Iran sanctions bill. A vote is expected before the end of the week.

The measures would cement into law existing sanctions over Moscow's aggression in Ukraine, which were imposed by Trump's predecessor, Barack Obama. That would make it harder for Trump to lift them unilaterally.

They would hit Russians accused of human rights abuses, supplying weapons to Syria's government, and conducting cyberattacks on behalf of Russia's government.

They would also sanction Russian mining, metals, shipping, and railway companies, going beyond the energy and financial firms previously targeted.

"The amendment to the underlying Iran sanctions bill maintains and substantially expands sanctions against the government of Russia in response to the violation of the territorial integrity of the Ukraine and Crimea, its brazen cyberattacks and interference in elections, and its continuing aggression in Syria," a group of Republican and Democratic senators backing the amendment said in a statement released on June 12.

Tillerson's comments echoed earlier comments by Defense Secretary Jim Mattis, who told House lawmakers on June 12 that Russian President Vladimir Putin didn't appear to want an improvement of relations with Washington.

"At this time … I do not see any indication that Putin would want a positive relationship with us," Mattis told the House Armed Services Committee. "That’s not to say we can’t get there as we look for common ground. But at this point, he has chosen to be competitive, a strategic competitor with us, and we’ll have to deal with that as we see it."

More Questioning

Tillerson’s testimony also comes as other administration officials faced more questioning from lawmakers on the issue of ties between associates of Trump and Russian officials, an issue that has dogged the White House since before Trump's inauguration.

Attorney General Jeff Sessions, who heads the Justice Department and nominally oversees the FBI, was set to testify publicly before the Senate Intelligence Committee later on June 13, about his interactions with Russia's ambassador to the United States.

Along with committees in the House and Senate, the FBI has been conducting a criminal investigation.

Trump fired FBI Director James Comey on May 9, and bragged to Russian officials a day later about it, according to a document of the meeting read to the media by a U.S. official.

During his June 8 Senate testimony, Comey suggested possible conflicts of interest or even obstruction of justice.

Sessions, meanwhile, had recused himself from oversight of the FBI's Russian probes, owing to his meetings with Russia's ambassador to the United States.

However, he ultimately co-signed the letter recommending Comey's firing, something Comey suggested was unusual.

Another former FBI director, Robert Mueller, was then appointed by the Justice Department to conduct the Russian investigation. That probe continues.