U.S. Rep. Joseph Kennedy III says he is still undecided about running for Senate, but has filed a statement of candidacy with a federal agency and formed an exploratory committee.

Kennedy, D-Brookline, on Monday filed with the Federal Election Commission, which tracks money raised and spent by candidates.

The filing does not necessarily mean he is definitely running, but allows him to raise money to explore the possibility. He also formed a campaign committee.

Earlier in the day he posted a message to voters on his Facebook page stating he is still considering whether to run and hasn’t reached a decision yet.

Running would mean taking on a fellow Democrat in the primary, Sen. Edward Markey, D-Malden.

The prospect of two well-known, well-financed Democrats fighting each other has some party leaders, including several locals, dismayed, and Kennedy acknowledged that in his post.

“I hear the folks who say I should wait my turn, but with due respect — I’m not sure this is a moment for waiting,” Kennedy wrote on Facebook.

“Our system has been letting down a lot of people for a long time, and we can’t fix it if we don’t challenge it. I’ve got some ideas on how to do that.”

He also said he didn’t expect to have to make a decision so soon.

It was his first public comment on the possibility of him running for Senate.

His potential candidacy became known when voters started being polled about a possible match between he and Markey.

Markey has shown no signs of backing down as he has hired some of the top political operatives in the state and gotten the endorsement from most Massachusetts members of Congress.

He has been emphasizing his backing by progresses, releasing a video last week with an endorsement by Sen. Elizabeth Warren, D-Mass., and on Monday announced one by Coalition for Social Justice.

Kennedy said family is a major consideration for him as he has two young children and a wife.

At present, his official position is that he is running for re-election to the House in the 4th District that includes the Attleboro area.

A decision on running for Senate will come soon, he said.

Jim Hand may be reached at 508-236-0399 or jhand@thesunchronicle.com. You can follow him on Twitter at @TSCpolitics.

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