The declaration came as members of Greece's new leftist government toured European capitals to make a plea for renegotiating conditions attached to its €240 billion ($270 billion) rescue package.
Though some countries have been sympathetic to the new Greek appeal for debt relief - with US President Barack Obama supporting the idea on Sunday - nations like Germany and Spain have insisted that Greece's new Syriza-led government respect the deal signed by its predecessors.
"Joining Europe is voluntary, and we belong to that club on the condition we respect the club's rules, because it is in everyone's interest we do so," Montoro told Spain's public television channel TVE.
"Europe is not the European Commission, nor the European Central Bank. We are Europe - the countries that compose it - and we are the ones who established the rules."
Montoro said Greece needed to respect the reforms and austerity bailout terms Athens had agreed with international creditors "as we did".
He said it was too easy for new governments to come to power in times of economic pain with promises to increase spending that earlier leaders had renounced with long-term interest in mind.
"We would all like to govern that way. But the question is, where will this money come from? From Greeks? From other Europeans? Who will be providing this money? That is the question," he insisted.
Spain's ruling conservatives have credited their austerity programme for the return of modest growth after six years of brutal recession - a fiscal hardline the government has stuck to despite rising public discontent.
But despite that revival in economic activity, unemployment in Spain remains at a dizzying 23.7 percent, and public services like education and health care have been hard hit by spending cuts.
Both the government and opposition Socialists face an election-packed calendar in 2015 fraught with risk, as the hard-left Syriza-allied Podemos party continues to gain backing in Spanish opinion polls.