World leaders led by Donald Trump have congratulated Boris Johnson on his election victory, with the US president reiterating his belief that Britain and the US would now be free to strike a “massive” trade deal after Brexit.

“Congratulations to Boris Johnson on his great WIN!” Trump tweeted. “This deal has the potential to be far bigger and more lucrative than any deal that could be made with the EU. Celebrate Boris!”

Trump and the British prime minister have stressed the importance of sealing a rapid US-UK free trade agreement as soon as possible after Brexit and the issue of the status of the NHS in any such deal became a significant theme of the election campaign.

Despite Johnson insisting the NHS was not for sale and Trump declaring he would not be interested in access to the NHS if it was presented “on a silver platter”, Jeremy Corbyn, the Labour leader, repeatedly pressed the prime minister on the question.

Angela Merkel congratulated Johnson on his “resounding victory” in a statement on Twitter by her spokesman. “I look forward to working with you for the friendship and strong cooperation between our nations,” the German chancellor said.

The Kremlin said it was not sure whether the Tory win would bring “good relations” with Russia, which have been strained in recent years. “I don’t know to what extent such expectations are appropriate,” said the Kremlin spokesman, Dmitry Peskov.

The Israeli foreign minister, Israel Katz, hailed Johnson’s larger than expected majority as “not just a political victory, first and foremost a victory of values”, referring to the allegations of antisemitism that dogged Corbyn throughout the campaign.

“The spectre of antisemitism loomed large, and the British public overwhelmingly voted against it in what is, in our opinion, a testament to British history and values,” Katz said. “It serves as an important milestone in the fight against hatred.”

India’s nationalist prime minister, Narendra Modi, also congratulated Johnson. “I wish him the best and look forward to working together for closer India-UK ties,” he tweeted.

Australia’s rightwing prime minister, Scott Morrison, tweeted: “Congratulations @BorisJohnson on a resounding victory. Looking forward to the stability this brings and a new deal for Oz with the UK. Say g’day to the quiet Britons for us.”

Conservative and nationalist leaders in eastern European, eager to remain close to the UK after Brexit, were enthusiastic about Johnson’s win. “There has been a fundamental change here. Boris Johnson and the Conservatives have won a clear majority,” said Poland’s prime minister, Mateusz Morawiecki.

In Hungary, the nationalist Fidesz party of the prime minister, Viktor Orbán, was quick to congratulate Johnson, with Katalin Novák, the minister for the family, youth and international affairs, tweeting: “Conservatives have to become stronger in Europe.”

The Czech prime minister, Andrej Babiš, said that while it was a pity for Europe, it was at least “clear that Britain is leaving”. Babis described Johnson’s triumph as “a crushing victory for a charismatic leader”.