Shia are believed to make up around 10% of Saudi Arabia's native population of 16 million and complain of being marginalised by a government closely attached to religious conservatives who consider Shia beliefs heretical.
Shia delegations from Saudi Arabia's oil-producing Eastern Province and its southern region of Najran have separately visited King Abdullah since his accession last month.
"Our visit was mainly about political prisoners, asking for their release," said Jaafar al-Shayeb, from the Eastern Province where most of the country's Shia Muslims live.
Five representatives from Najran's smaller Ismaili Shia community also handed Abdullah a list of requests 10 days ago when they met him to pledge allegiance.
Their requests included the release of prisoners, a bigger role in state affairs and the return of Shia they said were forcibly moved from Najran after a fierce government crackdown
five years ago.
Abdullah, who as crown prince launched a "national dialogue" two years ago that brought Saudi Sunnis and Shia together for talks, has overseen a modest easing of restrictions on Shia in the Eastern Province.
A think-tank warns of sectarian
strife if discrimination continues
When he succeeded his half-brother Fahd last month, he promised to work "to achieve justice and righteousness, to serve all people without discrimination".
Shayeb said the request for prisoner releases was prompted by a pardon Abdullah granted to five reformists a week after his accession, as well as an amnesty for several Libyans held over a suspected plot to assassinate him in 2003.
He said the Shia had asked for the release of 10 political prisoners. "There was a promise that they will review their cases," he said, adding that nothing yet had emerged.
Cabinet post demand
The petition from Shia in Najran, on the southern border with Yemen, asked that they be given a chance to serve in the cabinet, consultative shura council and other state bodies.
It also asked that prisoners jailed after the unrest in 2000 in Najran be included in Abdullah's amnesty and for "large numbers" of people transferred out of the province to return.
Last week a think-tank warned that Saudi Arabia - considered the birthplace of Islam - risked undermining a decade of mainly peaceful sectarian ties unless it offered Shia a bigger government role and curbed discrimination.
The International Crisis Group said the overthrow of Saddam
Hussein, ending decades of minority Sunni rule in neighbouring
Iraq, had emboldened Shia and heightened Sunni fears in