He told Reuters that the EU should not interfere with "domestic issues".
He said he had already won backing from Poland that it would veto any move to strip Hungary of its EU voting rights.
The EU objects to Hungary's tight controls on asylum seekers and non-governmental organisations (NGOs), as well as a higher education law.
Critics say the education law could lead to the closure of the prestigious Central European University, founded by philanthropist George Soros.
Thousands of Hungarians have held protest rallies against the laws in recent months.
Asked by Reuters on Monday whether Hungary would backtrack on any of the three issues, Mr Szijjarto answered: "No. Why should we?
"These laws belong to national competence, so I think European institutions should refrain from making attempts at interfering with domestic issues."
The minister added that "my Polish colleague" had made it very clear that Warsaw would veto any EU sanctions against Hungary.
EU rules envisage that such decisions as stripping a member country of its voting rights should be approved unanimously.
Hungary's right-wing Fidesz government of Prime Minister Viktor Orban is under sustained pressure from European institutions to withdraw the three laws, two of which have already been passed, the BBC's Nick Thorpe in Budapest reports.
Hungary is currently forcibly housing asylum seekers in secured shipping containers, raising serious questions whether it is compatible with EU law.
Hungary's Higher Education Law, signed in April, could force the closure of the Budapest-based CEU, which ranks among the top 200 universities in the world in eight disciplines.
Meanwhile, draft legislation on NGOs is expected to go before parliament soon.
Human rights groups say it would stigmatise them as "foreign-backed" organisations.
Last month, the deputy head of the bloc's executive Commission, Frans Timmermans, warned action would be taken in coming weeks if there were no positive developments.
Hungary passes bill targeting Central European University
Hungarian attack on George Soros prompts NGO anger
The university built to defend democracy
Hungary will not back down over three laws which have brought in question its future membership in the EU, Foreign Minister Peter Szijjarto says.