The Israeli government has asked Tzipi Livni, the leader of the opposition, to join the ruling coalition, according to local media reports.
The office of Benyamin Netanyahu, the prime minister, said in a statement on Thursday that the offer had been made.
"The prime minister asked Mrs Livni to join a national unity government ... in the face of the national and international challenges facing Israel today," a statement said.
Livni's office said that she responded to Netanyahu by saying, "If this is a serious offer, I have always said we can discuss the issue". However, she added that an internal Kadima party vote would decide any such move.
Livni's Kadima party has 28 MPs in the Knesset, the 120-member Israeli parliament, the largest number of any party.
She rejected an offer to join the ruling coalition, which contains Netanyahu's right-wing Likud party, the centre-left Labour, and far-right and religious parties, after elections in March.
Reports have surfaced in recent days that Netanyahu has attempted to persuade several Kadima MPs to join his coalition to weaken the opposition party.
Sherine Tadros, Al Jazeera's correspondent in Jerusalem, said that there is still a wide gulf between the position of the Kadima party, headed by Livni, and Netanyahu's right-wing coalition government.
"Chief amongst those differences is the issue of the Palestinians and what is on the table when it comes to negotiating with them," she said.
"Livni has always maintained that everything has to be on the table when Israel negotiates with the Palestinians - including Jerusalem, the borders and settlements.
"And this is why she did not join the coalition government back in March when it was being formed."
Tadros added that there has been no recent indication that Netanyahu would accede to Livni's demands.
"We also saw a very heated discussion on Wednesday in the Knesset where Livni took Netanyahu to task over his foreign policy, very much calling it a failed foreign policy."
Tadros said that the offer was made either to weaken Kadima or because Netanyahu may want the support of more centrist politicians in order to push through centrist policies in parliament, such as a 10-month settlement construction suspension and to aid a deal with Hamas, the Palestinian group, for the captured Israeli soldier Gilad Shalit.
According to Netanyahu's office Livni has not been offered a ministerial position so far.
The prime minister said to Livni that a future unity government would be based on his vision of both a Jewish and Palestinian state existing side-by-side.