In a statement, it said Boko Haram - which pledged allegiance to IS in 2015 - continued to "undermine the peace and stability" in West and Central Africa.
Meanwhile, a senior US official said there were reports of Boko Haram fighters joining IS in Libya.
Nigeria is to host a summit on Saturday on fighting Boko Haram.
President Muhammadu Buhari will welcome counterparts from Benin, Cameroon, Chad and Niger for the gathering in Abuja, along with French President Francois Hollande, UK Foreign Secretary Philip Hammond and US Deputy Secretary of State Antony Blinken.
In the statement, the 15-member UN Security Council expressed "alarm at Boko Haram's linkages with the Islamic State".
It also voiced its support for Nigerian President Muhammadu Buhari's "crucial initiative" to hold the security summit in Abuja.
Meanwhile, Mr Blinken - who is already in Nigeria - said he was concerned by reports that Boko Haram militants were going to Libya, where IS influence has grown in recent months.
"We've seen that Boko Haram's ability to communicate has become more effective," he said.
"They seem to have benefited from assistance from Daesh [IS]."
Mr Blinken added: "So these are all elements that suggests that there are more contacts and more co-operation, and this is again something that we are looking at very carefully because we want to cut it off."
At the same time, he declined to comment on whether the US would agree to a Nigerian request to sell it American war planes to fight Boko Haram.
Who are Boko Haram?
Boko Haram militants have been attacking civilian targets as the Nigerian military seeks to wrest territory from their control.
The Islamist group's seven-year insurgency has killed some 20,000 people and driven more than two million people from their homes.
The UN Security Council has said it is alarmed by ties between Nigeria's Boko Haram Islamist militants and the Islamic State (IS) group.