"As for top-level contacts, I am not against them", Putin said about talks with Poroshenko, according to the Russian state-run news agency TASS.
The vessels were on a mission to sail from the Black Sea into the Sea of Azov and were operating in line with a 2003 treaty with Russian Federation that gave Ukrainian ships free passage through the strait.
Ties between Ukraine and Russian Federation have been damaged by Russia's 2014 annexation of Crimea and support for armed rebels in eastern Ukraine. Fighting there has killed at least 10,000 people since 2014 but eased somewhat after a 2015 truce.More news: US Secretary of State Pompeo defends Saudi crown prince
The Ukrainian seamen have been put in custody for two months pending Russia's investigation into the clash. Russian Federation completed a bridge between the peninsula and its mainland earlier this year.
Stoltenberg said that he expects the ministers, meeting in Brussels, to signal that "we are ready to receive the first annual national program" from the ethnically-divided country, which was riven by war in the 1990s when the former Yugoslavia broke apart. They are charged with "illegal border crossing". A criminal case has been launched over the violation of Russia's state border.
In Russia, Moscow's top rights official Tatyana Potyaeva visited the three wounded Ukrainian sailors who are being treated for hand, arm and leg injuries in the medical unit of the Matrosskaya Tishina remand prison.
Mathieu Boulegue, a research fellow with Russian Federation and Eurasia program at London's Chatham House think tank, said Poroshenko's move appeared to be "an attention-seeking reaction" that is likely to antagonize Moscow even further and play badly with the worldwide community. Two of them also spoke to their relatives, she added.More news: Deontay Wilder vs. Tyson Fury
Moscow called the incident a provocation, while Kiev denied any wrongdoing.
Ukrainian President Petro Poroshenko on Monday submitted to parliament a draft law on ending the Treaty on Friendship, Cooperation and Partnership between Ukraine and Russian Federation, the parliament's press service said. "The Russians behaved in a way that is deeply inconsistent with worldwide law". Ukraine says the attack occurred in global waters.
The naval confrontation between Russian Federation and Ukraine was one of the top issues on the agenda of foreign ministers and diplomats from 29 North Atlantic Treaty Organisation members who are meeting in Brussels on December 4.
North Atlantic Treaty Organisation foreign ministers are expected Wednesday to activate Bosnia's Membership Action Plan, a reform process that prepares countries for membership.More news: Aust women take bronze at Dubai Sevens
Ukraine has accused Moscow of blocking commercial vessels from entering and leaving the ports.