The Hungarian prime minister, Viktor Orbán, has thanked Conservative MEPs for their “solidarity” in voting against European Union action to protect the rule of law in his country.

In a signed letter to MEPs who voted with his Fidesz party, Orbán expressed his appreciation of “the support you’ve shown towards national sovereignty and solidarity during the vote”.

The European parliament voted earlier this month to launch the EU’s sanction process against Hungary, after concluding there was “a clear risk of a serious breach” of the EU’s democratic values. Most British Conservative MEPs opposed the plan.

Based on the findings of international observers, a European parliament report on Hungary listed concerns about the erosion of judicial independence, decline of press freedom, growing corruption, increasing xenophobic attacks on migrants, including asylum seekers. It also accused Orbán of attacks on the billionaire philanthropist George Soros that included “clearly antisemitic stereotypes”.

Writing to MEPs who supported him, Orbán expressed his gratitude. “I can assure you that regardless of the shameful attacks of pro-immigration forces, we will not give in to extortion. We will continue to fulfil our European obligations and defend the borders of European and Hungary, for the sake of our citizens.”

“I wish you good health and much success in your highly responsible duties,” it concludes.

The letter was first reported by Yahoo! News.

Two Conservative MEPs abstained from voting with Orbán. Another two, who are currently suspended from the Conservatives’ European parliamentary group, because of their stance on Brexit, voted to start the sanctions procedure against Orbán.

One of the rebels, the MEP for South West England and Gibraltar, Julie Girling, told the Guardian last week that the Orbán vote was a further sign that the “hard-right of the party had seized control of the agenda”. Echoing this view, a former leader of the Conservatives in Brussels and Strasbourg, Edward McMillan-Scott, said he no longer recognised the party he had been a member of for 25 years.

The Conservatives have also been criticised by political opponents for “trampling on the legacy” of previous Tory governments, which promoted democracy in central and eastern Europe.

The Conservatives staunchly reject these assertions, arguing that triggering the EU sanctions procedure would do nothing to change Orbán’s behaviour.

In response to the criticism, the Conservative home affairs spokesman in the European parliament, Daniel Dalton, has written: “We take very seriously the concerns about the direction that the Hungarian government is taking, particularly in the rhetoric surrounding migrants and ethnic and religious minorities, and the rule of law and freedom of the press.”

A Conservative spokesman played down the letter. “This is a round robin letter sent to MEPs of all parties who voted against the motion. As we have made clear, our vote in no way signalled approval or support for any of the policies of the Hungarian government. On the contrary we opposed the resolution because it will not work and could make any subsequent legal moves against Hungary more difficult.

“We take very seriously the concerns about the direction of the Hungarian government. That means it is even more important that action that might ultimately be taken has a sound legal base and is able to make a difference.”