Palestinian Prime Minister Ismail Haniya of the ruling Hamas group has said he is willing to resign if this will end a Western aid boycott.
Mr Haniya said the US did not want him to lead any unity government
His comments came after talks on a unity government with Palestinian Authority President Mahmoud Abbas.
Sanctions were imposed this year by Israel and Western countries, which see Hamas as a terrorist organisation.
"If we have to choose between the siege and myself, we must lift the siege and end the suffering," Mr Haniya said.
The US and Europe imposed crippling sanctions on the authority in March because Hamas refused to recognise Israel, renounce violence and respect previous Israeli-Palestinian agreements.
Speaking outside a Gaza mosque, Mr Haniya said the West had made it a condition that "the siege will not be lifted unless the prime minister is changed".
But Mr Haniya said the discussions on forming a unity government were yielding results and that he hoped a new cabinet could be in place within three weeks.
Correspondents say the statement could be a sign that the Hamas and Fatah factions could be inching closer towards a deal.
It was hoped that the formation of a unity government would lead to direct foreign aid being resumed.
But weeks of on-off negotiations punctuated by political and security crises have failed to achieve a breakthrough.
Hamas insists it will never join a government that recognises the State of Israel.