Mr Todd says his desire for more officers has been frustrated
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Greater Manchester Police is the most under-funded in the country, according to its chief constable.
Michael Todd was speaking in an exclusive chat with the BBC's Manchester website.
He said he wanted to recruit 3,000 more officers, but the government refused to pay for the increase.
"We have been the most under-resourced force in the country and also a force with some of the most difficult demands on it," he said.
There are currently 8,000 officers in Greater Manchester Police (GMP), but Mr Todd wants to see this figure rise to 11,000.
Mr Todd said he recognised how people in communities where crime was high were frustrated by the lack of officers, but added the force was doing the best job it could.
"We have had to prioritise to deal with serious crime and have not been able to meet all of the community demands, which I do want to and I do think are reasonable," he said.
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We are trying to return as many officers as possible to the streets to provide the reassurance that our communities want
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"I want a return to the real bobby on the beat who knows the community, deals with their problems and ensures they feel safe.
"The problem is, we have to pay for it. That is another problem - but one I will continue to fight for."
In response to a web chatter who said he was frustrated because he wanted to apply to GMP, but his application had been delayed because of funding, Mr Todd said: "It is very frustrating for me.
"GMP has been under-resourced for years and last year we started to make up some of that ground.
"Sadly this year we have not been allowed to move further forward.
"This does mean that some who wish to join us will have a longer wait than I would have wanted. I wish you could join us right now."
Cycle patrol
He added the visible police presence on the street had increased since he took over at GMP in October 2002, with 600 new police officers on the beat.
"We are trying to return as many officers as possible to the streets to provide the reassurance that our communities want," he said.
"I was out on cycle patrol myself in Oldham the other week and saw the public reaction.
"We do need more officers out there and that is what we are seeking."