The two leaders held separate meetings with European Union foreign policy chief Josep Borrell before a three-way session in North Macedonia.
A news conference was scheduled for after the meeting, but as talks continued into the night, it was not clear when it would take place.
"I am optimistic," Kurti said ahead of the meetings in the lakeside town of Ohrid in North Macedonia.
"I came here with a good aim, with a good will and with trust that what was agreed before...will continue here through the talks for the implementation plan, and in this way have a final deal on the normalisation."
Kosovo declared independence in 2008, almost a decade after a guerrilla uprising brought an end to repressive Serbian rule.
Kosovo and Serbia agreed in Brussels last month to a Western-backed deal to normalise relations, following nearly 10 years of EU-mediated dialogue during which little progress was made. However, agreement is still needed on an annex on implementing the plan, which will be the focus of Saturday's discussions.
Despite verbal consent to the agreement, Kurti and Vucic remained firm in their positions without any hint they were willing to compromise on key issues.
Vucic has said Serbia would never accept independence of Kosovo, while Kurti has said he would not agree to a proposed association of Serb municipalities in Kosovo, which would give greater autonomy to Serb majority municipalities.
Thousands protested in Belgrade on Friday against the EU plan which they see as de facto recognition of Kosovo independence.
"The eyes of the EU & the Western Balkans are on Ohrid today," Borrell tweeted.
Belgrade and Pristina need to mend bilateral ties for both to achieve their strategic goal of joining the EU.
"I want to caution that we may not have a final agreement," Gabriel Escobar, the senior U.S. diplomat for the Western Balkans who is also attending the Ohrid talks, told Pristina-based RTV21 station.
"We are going to work towards finalising the annex, but I expect a lot of progress."
NATO bombed Serbia in 1999 in response to the expulsion of Kosovo's majority Albanians by Serb forces after which Belgrade lost control of its southern province.
(Reporting by Fatos Bytyci; Additional reporting Sabine Siebold and Ivana Sekularac; Editing by Kirsten Donovan and Emelia Sithole-Matarise)
By Fatos Bytyci