Shipping traffic has resumed to and from Ukraine’s ports on the Sea of Azov following a standoff with Russia, a Ukrainian minister has said.

Commercial ships were moving through the Kerch strait linking the Sea of Azov with the Black Sea, said the infrastructure minister, Volodymyr Omelyan.

Omelyan, who accused Russia last week of blocking Ukrainian cargo trying to pass through the strait, said the ports of Berdyansk and Mariupol were partially unblocked thanks to a “stern international response”.

Later on Tuesday, the Ukrainian agriculture ministry said grain was again being loaded on to ships in the two ports. and the passage of ships with agricultural products through ports on the Sea of Azov had been unblocked.

Russia, however, insisted it never blocked vessels from sailing through the strait and that any possible disruptions were due to bad weather.

The tug-of-war between the neighbouring countries over Russia’s annexation of Crimea and support for separatist rebels in eastern Ukraine escalated after an incident on 25 November in which the Russian coastguard fired upon and seized three Ukrainian naval vessels and 24 sailors onboard.

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 Russia that gave Ukrainian ships free passage through the strait. But Russia, which annexed Ukraine’s Crimean peninsula in 2014, claimed the Ukrainian boats entered its territorial waters without permission.

The US and its allies have condemned what they described as unjustified use of force by Russia and urged it to release the ships and their crews.

Nato foreign ministers were meeting the Ukrainian foreign minister, Pavlo Klimkin, on Tuesday and Wednesday as Ukraine seeks international backing over the standoff with Russia.

Speaking before the meeting, the Nato secretary general, Jens Stoltenberg, urged Russia to release the Ukrainian sailors and ships and allow free navigation and unhindered access to Ukrainian ports in the Sea of Azov.

The Ukrainian president, Petro Poroshenko, responded to the standoff by introducing martial law for 30 days, a measure Ukraine had not taken even after Crimea’s annexation and amid large-scale fighting between Ukrainian forces and Russia-backed separatists in 2014-15.

As part of martial law, Ukraine has strengthened its forces on the border with Russia, called up reservists for training and barred entry to all Russian males aged between 16 and 60.

Some critics at home, including Poroshenko’s main political rival, the former prime minister Yulia Tymoshenko, accused him of using the naval incident for political purposes before March’s election. But Poroshenko has pledged that martial law would not interfere with the vote.

The Kremlin has called the naval incident a provocation intended to shore up Poroshenko’s sagging popularity.

The lower house of Russian parliament, the state duma, approved a statement on Tuesday accusing the Ukrainian president of a “reckless and cynical attempt to change the situation in his favour”, and a “desire to cling to power at any cost even at the threat of a full-scale war”.

The European court of human rights on Tuesday also demanded that Russia provide adequate medical care to the sailors arrested and wounded in last month’s clash.