* PM says quitting would be irresponsible, destablising
* PM proposes talks with protesters on Monday
* Pledges replacement for head of state security
Thousands of Bulgarian protesters demanded the resignation of their new Socalist-led government on Sunday, but the prime minister dismissed the prospect of stepping down as "highly irresponsible" and "destabilising".
The two-week-old government bowed to public anger on Saturday to reverse its appointment of a powerful media figure and coalition ally to lead state security after rushing the move through parliament on Friday.
Some 15,000 protesters poured onto the streets of Bulgaria's capital Sofia for a third day on Sunday, chanting "Resignation" and "Red trash".
The previous government of the centre-right GERB party was forced to resign in February after mass protests over living standards and a failure to tackle graft, and that dismay with the political class has persisted with the new administration.
GERB became the biggest party in parliament after an election last month, but failed to secure a majority, leaving the Socialists to assemble a coalition that relies on the passive support of a small nationalist party.
Many of the protesters demanded changes in the electoral law to give new, smaller parties that are not part of the entrenched elite a chance of winning seats in parliament.
Six years after joining the EU, the Balkan country is still its poorest member, with widespread graft and organised crime deterring investment and barring it from joining the passport-free Schengen zone.
Protests were also held in several other cities.
The government, backed by the ethnic Turkish MRF party, promised on Saturday to replace Delyan Peevski, also a MRF deputy, as head of the powerful agency for national security.
On Sunday, Prime Minister Plamen Oresharski promised to seek public support for a new nomination and invited protest leaders for talks on Monday, as well as dismissing talk of resigning.
"To resign will be an easy personal decision, but it will be highly irresponsible because of the danger of again destabilising the country," he said in a statement.
Oresharski warned that the collapse of the government would deprive Bulgaria of billions of euros in EU aid, as the funds have to be negotiated by the end of the year.
That could further erode gross domestic product per capita, already less than half of EU average.