The US on Monday said Russia would put at risk any hope for more constructive relations if it used its UN veto to shut the sole border crossing for aid into Syria.
Secretary of State Antony Blinken joined Italy in hosting talks on the US-led coalition to defeat ISIS, during which he discussed the Bab Al Hawa crossing on the Syrian-Turkish border.
Mr Blinken said in Rome that it was crucial to broaden "cross-border assistance, which is essential in reaching millions of Syrians who are in dire need of food, medicine, Covid vaccines and other life-saving aid".
The crossing is due to close on July 10 without UN authorisation for another year and Russia – which has already succeeded in reducing the border openings to one – has not ruled out using its veto to block an extension.
Russia and Iran are the chief supporters of Syrian President Bashar Al Assad, who has wrested back control of most of Syria after a decade-long civil war.
They say Damascus should have sole control over aid deliveries.
"What's been made clear all the way from the president all the way down to much lower-level officials to the Russians and to others is that we want to have a constructive relationship with Russia on the areas on which we can work together, and we think Syria ought to be one of them," a senior official who accompanied Mr Blinken said.
"But the test is going to be whether or not we can maintain and expand these cross-border mechanisms.
"If we're not able to work together on this basic human need, that would make it very difficult to work on anything else with the Russians with regard to Syria more broadly."
US President Joe Biden raised the issue when he met Russian leader Vladimir Putin on June 16 in Geneva.
Both presidents voiced hope that the summit would bring more stability to US-Russia relations after months of tension.
UN Secretary General Antonio Guterres last week urged all Security Council members to reach a consensus to preserve the crossing, which allows aid to reach about three million people in the Idlib region.