The recommendation came in a resolution adopted by the 15-member council without a vote. Montenegro's application now goes to the General Assembly for final approval.
UN spokeswoman Marie Okabe told reporters the assembly was expected to take up the matter next Wednesday wit approval a foregone conclusion.
In a statement read out by Danish Foreign Minister Per Stig Moller, the council said it noted "with great satisfaction the republic of Montenegro's solemn commitment to uphold the purposes and principles of the Charter of the United Nations and to fulfill all the obligations contained therein."
Republics join hands
Serbian Foreign Minister Vuk Draskovic and his Montenegrin counterpart Miodrag Vlahovic signed a protocol establishing diplomatic ties between the two republics.
"Political parties, decisions... everything is temporary, but special relations between Serbia and Montenegro are not," said Mr Draskovic after the signing of the protocol.
"No one never must cast a shadow on relations between Serbia and Montenegro," he added as the two ministers drank a champagne toast, marking the occasion.
Mr Vlahovic said the two republics "are together again in the capacity which enables them to be equal."
"Montenegro has not fulfilled its independence to build a fence around itself or to rise up barriers, but on the contrary, to cooperate," he said.
Montenegro held a referendum on independence on May 21, in which 55.5 percent of voters opted to break away from Serbia. The threshold for the "Yes" vote to be validated was 55 percent.
Serbia relents
On June 3, after more than eight decades of union, Montenegro's parliament proclaimed independence, although Serbia only officially recognised it 12 days later.
Belgrade had openly supported those in Montenegro who had opposed separation, with Prime Minister Vojislav Kostunica, a moderate nationalist, hardly hiding his dissatisfaction with the outcome of the vote.
Serbia and Montenegro have been united in various forms since 1918. Their last joint state was a loose union that had replaced the rump Yugoslavia in 2003.
The vast majority of their populations share the same culture, language and Orthodox Christian faith.
Mr Vlahovic said that "Montenegro will be the best and the closest neighbour to Serbia and to everyone who lives there."
"We agreed that the people and their rights in the respective republics should be protected and improved," he said.
The two ministers agreed that they would send ambassadors "as soon as possible," with Mr Vlahovic adding that this could be expected in September.
The independence of Montenegro, a nation of just 650,000 wedged between the mountains and the Adriatic Sea, ended the painful, 15-year dissolution of the former communist Yugoslavia, after Bosnia, Croatia, Macedonia and Slovenia went their separate ways in the early 1990s.
The world's newest country has been recognised in recent days by the European Union, the United States, Russia, China, Denmark, the Czech Republic, Italy and Turkey; by regional southeast European neighbours Albania and Greece; and by the other former Yugoslav republics: Serbia, Bosnia, Croatia, Slovenia and Macedonia.