The US, which has played a mediation role in the talks, said it was studying the Hamas response and would discuss it with Middle East allies.
Amid diplomatic manoeuvres in the push for an end to the Israel-Palestine conflict, Middle East expert John Strawson says the crisis has reached a critical moment.
On their second day of truce talks in Cairo with Egyptian and Qatari mediators, Hamas negotiators maintained their stance that any truce agreement must end the war.
Jamaica joins a list that includes some 140 UN member states and the 11 Caribbean Community (CARICOM) countries.
The US is the only country that abstained from voting and did not veto the resolution as it has done in the past.
This comes after Russia and China on Friday vetoed a US-led draft resolution that condemned a recent attack by Hamas but did not explicitly demand an immediate end to Israel's campaign in Gaza
The product of more than a month of negotiations and the exchange of updated drafts among council members, the final text reflects growing concern and international outrage over the worsening humanitarian catastrophe in the southern Gazan city of Rafah.
A total of 127 people died in 24 hours, Hamas-run Gaza's health ministry said, as the main battlefront edged closer to far-southern Rafah, where 1.4 million Palestinians live
CIA Director William Burns was due in Cairo Tuesday for a new round of talks on a Qatari-brokered ceasefire proposal that would temporarily halt fighting in exchange for Hamas freeing hostages.
The countries are the US, Australia, Britain, Canada, Finland, France, Germany, Italy, Netherlands and Switzerland. They have welcomed investigation into the allegations that some UNRWA staff took part in Hamas's October 7 attack.
Israel's ensuing military offensive has killed at least 26,422 people, most of them civilians, in Gaza, according to the health ministry in the Hamas-run territory.