The 84-year-old's announcement comes at a moment of soul searching for the Democratic Party, after the GOP swept both chambers of Congress and won the presidential election in November.
But the senior senator said twice on Sunday that no gun control legislation would have stopped the mass shooting.
The mere implication that Trump could be a "good president" drew the ire of state Senate president Kevin de León, whose recent two-day trip to Washington was seen as laying the groundwork for a potential Senate run.
"Right now we are seeing one president changes actions of a president that came before him and that would happen in this area", the senator said.
Brandon Weeden keeps getting hired, now with Titans
Mariota suffered the hamstring injury on his second-quarter touchdown run in the Titans' 57-14 loss to the Texans on Sunday. He started 20 games in Cleveland, going 5-15 while throwing more interceptions than touchdowns.
Feinstein's old-school political sensibilities and foreign policy could be at odds with California, where increasingly young and diverse voters have demanded all-out opposition to Trump. "We are better off with her leadership and I look forward to continuing to fight together for California in the Senate".
On Sunday, Feinstein hinted in a national television interview that she was likely to run again, telling NBC's "Meet the Press" that she was close to a formal decision.
Los Angeles Mayor Eric Garcetti is reportedly hosting a fundraiser for Feinstein.
Texas at Iowa State
Texas coach Tom Herman gave credit to Iowa State's defensive game plan and acknowledged his team's mistakes and shortcomings. The teams combined for 568 total yards and 37 first downs, which is about one team's total in a typical Big 12 game.
Henry Bolton elected the new leader of UKIP in shock result
UKIP has held its third leadership contest since the European Union referendum - with a shortlist of seven candidates taking part. Mr Bolton did, however, signal he could be the latest in a long line of Ukip leaders to act as a scourge of liberals.
Las Vegas shooting suspect Stephen Paddock: What to know
Investigators reached Marilou Danley early Monday but do not believe she was involved in the shooting at this time . In a statement read by her lawyer, Ms Danley explained that she didn't know Paddock was planning a mass shooting .
Huge demonstration against Catalan independence in Barcelona
Some of Catalonia's biggest businesses began taking steps to transfer their registered headquarters to other cities in Spain. This weekend, Rajoy told Spanish newspaper El Pais that any declaration of independence by Catalonia would be rejected.