Ahmet Davutoglu, Turkey's foreign minister, said on Thursday that the resolution could damage ties between the two Nato allies.
Davutoglu said: "If it passes, then the [Barack] Obama [the US president] administration should try to prevent it from being voted by Congress."
Abdullah Gul, the country's president, was reported to have phoned Obama late on Wednesday to discuss the matter.
Turkey's Hurriyet newspaper said Gul had urged the US leader to use his influence to block the resolution.
Nancy Pelosi, the House speaker, has said she will wait to see the result of the committee vote before deciding whether to bring it to the House floor.
Armenian-US groups have for decades sought congressional affirmation of the killings as genocide.
Historians estimate that up to 1.5 million Armenians were killed by Ottoman Turks around the time of the First World War, an event widely viewed by scholars as the first genocide of the 20th century.
Turkey denies that the deaths constituted genocide, saying the toll has been inflated and that many of those killed were victims of civil war and unrest.
After decades of hostility, Turkey and Armenia signed a deal in October to establish diplomatic relations and open their border.
But the process has hit the rocks, with Ankara accusing Yerevan of trying to tweak the terms of the deal and Armenia charging that Turkey is not committed on ratifying the accord.
"We have taken very important steps for comprehensive normalisation in the Caucasus. It is necessary to avoid risking these efforts," Davutoglu said.
The minister did not say what Turkey would do if the bill was adopted, but a Turkish official, speaking on condition of anonymity, said "all options are on the table", including once again recalling Turkey's ambassador to the US.