Vitaly Churkin, the Russian ambassador to the UN, said on Wednesday: "We do not feel any need for big moves now. As far as we are concerned. everything is working fine now [between Lebanon and Syria]."
But John Bolton, the US ambassador to the UN, said the text backed by London, Paris and Washington would soon be circulated among the council's 15 members and he hoped for "fairly prompt action".
Agreement among the three had been hampered by differences between the US and France over the text's breadth.
But Condoleezza Rice, the US secretary of state, and Philippe Douste-Blazy, the French foreign minister, worked out the details of the draft embraced by the three countries over dinner on Tuesday.
The State Department said on Wednesday that Rice and Douste-Blazy had reached broad agreement on future diplomatic steps to curb Syrian interference in Lebanon.
"There is no need whatsoever from Rice or Douste-Blazy to interfere in the internal affairs of Lebanon and in the affairs between Syria and Lebanon"
Syrian deputy foreign minister
Sean McCormack, the State Department spokesman, said the US hopes for quick approval of a new UN Security Council resolution on Lebanon, which probably would urge Syria to open diplomatic relations with Lebanon.
Council diplomats said the compromise draft would not mention Iran or Hezbollah - the Iranian- and Syrian-backed militia in south Lebanon - by name.
Syria, for its part, had argued that setting borders and diplomatic ties were none of the council's business.
Faisal Mekdad, the Syrian deputy foreign minister, said in New York that the Security Council, and especially the US, should stop interfering in Lebanon-Syria relations.
"There is no need whatsoever from Rice or Douste-Blazy to interfere in the internal affairs of Lebanon and in the affairs between Syria and Lebanon," Mekdad said.
Syria withdrew from Lebanon in April 2005. The two countries have not had embassies on each other's territory since Western powers carved the two states out of the remnants of the Ottoman empire in 1920.
Damascus says its many bilateral ties with Beirut are enough for now.