Markovic is thought to be in Russia
Serbia's deputy prime minister has accused the family of former Yugoslav President Slobodan Milosevic of ordering the assassination of a political opponent whose remains were discovered last week.
Serbian police said on Saturday they have "credible suspicions" that Mr Milosevic's wife, Mirjana Markovic, was involved in the death of former Serbian President Ivan Stambolic, who disappeared in 2000.
Ms Markovic has refused to return immediately to Serbia from Russia for questioning, according to the couple's daughter, Marija Milosevic.
The Serbian interior ministry has sent a subpoena to Ms Markovic through a lawyer summoning her to Belgrade.
"If she does not answer in the shortest possible time an international warrant for her arrest will be issued," officials said in a statement.
Marija Milosevic told the Montenegrin daily Publika that her mother was "surprised" by the threat.
"Let them (police) issue the warrant," she quoted her mother as saying during a telephone conversation from Russia.
Officials say they think Mirjana Markovic left the country on 23 February.
Interior Minister Dusan Mihajlovic said Mr Stambolic, an ally-turned-opponent of Mr Milosevic, had been kidnapped and shot dead by special police loyal to the former Yugoslav leader.
He said he had been buried in quicklime in a pit in hills near the northern city of Novi Sad.
Media reports said police had searched the Milosevics' Belgrade home and the couple's home town of Pozarevac for Ms Markovic.
1975: becomes Serbian PM
1986: becomes Serbian president
April 1987: Milosevic embraces nationalism
December 1987: Stambolic dismissed as president
1997: dismissed from Yugoslav Bank for International Co-operation
August 2000: disappears
March 2003: remains found
Mr Stambolic disappeared while jogging in Belgrade two months before the October 2000 presidential election, which led to Mr Milosevic being driven from office.
There was much speculation at the time that Mr Stambolic would run against Mr Milosevic.
The discovery of his remains comes during an unprecedented police crackdown on organised crime and the "remnants of the Milosevic regime", sparked by the killing of Prime Minister Zoran Djindjic on 12 March.
Overall more than 1,000 people have been arrested, and some 400 have been charged.