Max Rossi / Reuters

Cardinal Roger Mahony, shown here arriving at Saint Peter's Basilica on Wednesday, says a conclave date will be set soon.

American Cardinal Roger Mahony tweeted Thursday that his fellow princes of the church are close to setting a date for the conclave that will choose the next pope, but the day ended without it happening.

Andrew Medichini / AP

Vietnamese Cardinal Jean-Baptiste Pham Minh Man arrives at the Vatican on Thursday. He was the last of the 115th electors to arrive in Rome for the conclave.

"Days of General Congregations reaching a conclusion. Setting of date for Conclave nearing. Mood of excitement prevails among Cardinals," wrote Mahony, who was stripped of his public duties in January over his handling of sex abuse claims in Los Angeles. He still retains a vote in the conclave.

Mahony took to Twitter a day after all cardinals agreed to a media blackout after concern was raised that some of them -- chiefly the Americans, who held two press briefings -- were talking too much.

His prediction that the pre-conclave meetings, known as general congregations, were almost over came as the last of 115 voting cardinals finally arrived in Rome from Vietnam.

The cardinals have been meeting each day since Monday to discuss church business under an oath of secrecy. At Thursday morning’s session, they focused instead on a report from the Vatican Secretary of State, Cardinal Tarcisio Bertone, about the state of Vatican finances. Sixteen cardinals spoke, some of them about what attributes the next pontiff should have.

The cardinals had a second session in the afternoon, after which it was announced no date had been set. They meet again Friday.

Vatican watchers have said that the insider cardinals who control the Roman Curia, the bureaucracy of the Vatican, are hoping for a quick conclave to keep outsider candidates from coming to the fore.

NBC News' Claudio Lavanga contributed to this report.

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This story was originally published on Thu Mar 7, 2013 11:16 AM EST