The resolution, which could be debated by the House on Tuesday, calls on the president to classify the massacre, in which as many as 1.5 million Armenians died, as a genocide.
Turkey in the past has warned that the resolution would harm ties with the US, and in March it withdrew its ambassador after the House foreign affairs committee approved the proposed resolution.
Davutoglu said he had discussed the resolution with US Secretary of State Hillary Clinton and urged her to spare no effort in preventing the resolution.
The World War I-era killings remain a major point of friction between Armenia and Turkey, with Yerevan saying about 1.5 million people were killed during massacres and forced marches.
Ankara acknowledges the deaths of between 300,000 and 500,000 Armenians, but says it was not a campaign of extermination.
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