(Recasts with litigation filed)
Aug 5 (Reuters) - Puerto Rican officials filed two separate lawsuits on Monday asking the bankrupt U.S. territory's supreme court to remove newly installed Governor Pedro Pierluisi from office on constitutional grounds, raising the prospect of more political instability on the island.
Puerto Rico Senate President Thomas Rivera Schatz asked the high court to hear the lawsuit he filed on behalf of his legislative chamber, and San Juan Mayor Carmen Yulin Cruz filed the second. The supreme court has the option of taking them up directly.
Pierluisi, 60, was hand-picked by his predecessor, Governor Ricardo Rossello, as secretary of state, making him first in line for governor when Rossello resigned on Friday.
After his nomination was confirmed by the Puerto Rico House, Pierluisi was sworn in as governor on Friday, even though the Senate had yet to ratify the appointment.
The Senate was to meet in a special session later on Monday.
"If the Senate decides to take any type of voting action on my governorship, I will respect the result of such vote," Pierluisi said in a Twitter message on Monday.
If Pierluisi steps aside, Justice Secretary Wanda Vazquez would become governor.
In a lawsuit initially filed on Sunday in a San Juan court, Schatz asked for an injunction ordering Pierluisi "to cease and immediately" give up the office and functions of governor.
The lawsuit contends that Pierluisi's swearing-in was void because the U.S. territory's constitution requires him to have fully taken the position of secretary of state before Rossello's resignation in order for him to become the new governor.
"That has still not happened yet because the Senate of Puerto Rico has not finalized its constitutional responsibility for advice and consent for such an appointment," it added.
Separately, Cruz, San Juan's mayor, petitioned the high court to end the "unconstitutional exercise of the Puerto Rico governorship."
Pierluisi said on Monday that he was sworn in as secretary of state when both legislative chambers were in recess, giving him "full possession" of the post under law.
He said he was properly sworn in as governor under Puerto Rico's constitution and a 2005 law that Schatz's lawsuit claims is unconstitutional.
Pierluisi's appointment has been controversial mainly because he formerly gave legal advice to the island's unpopular, federally created board supervising its finances, including its bankruptcy cases in federal court.
His installment as governor capped a week of political chaos after Rossello said he would resign over offensive chat messages that drew around a third of the island's 3.2 million people to the streets in protest.
The chats between Rossello and top aides took aim at female politicians and gay celebrities like Ricky Martin, and also poked fun at ordinary Puerto Ricans.
Publication of the messages unleashed local anger building for years over the island's painful bankruptcy process, ineffective hurricane recovery efforts and corruption scandals linked to a string of past governors, including Rossello's father. (Reporting by Luis Valentin Ortiz in San Juan; additional reporting by Karen Pierog in Chicago; editing by Andrew Cawthorne and Dan Grebler)