The equipment to be transferred will include night-vision goggles and rubber-coated steel bullets.
Barak also plans to grant thousands of permits for Palestinian labourers to work in Israel, the Associated Press reported defence officials as saying.
The Israeli defence minister has made similar pledges in the past without taking action.
Both sides had agreed to hold regular meetings following the US-sponsored Annapolis talks in November last year.
However, The Palestinian interior ministry reacted angrily to the police deployment, saying it was not up to Israel to dictate where its security forces were sent.
The Palestinian populace remains sceptical, as similar deployments have not prevented Israel from carrying out regular raids and assassinations in the past.
The move would be similar to that of 700 policemen deployed to Nablus last year.
Reporting from Nablus, Nour Odeh, Al Jazeera's correspondent, said: "If you ask people here, they do not feel any safer now than they did when Israel was in full physical control of the city - because nearly every night there is a new Israeli raid."
One Palestinian woman in Balata Refugee camp, which is adjacent to Nablus, told Al Jazeera that the promise of security from increased Palestinian forces was a non-starter.
"When Barak wants he sends in his troops and all we can do is hide and our leaders and police do the same," she said.
The officers ear-marked for Jenin have been receiving special training in neighbouring Jordan since January under a program funded by the US.
US officials said the men are not expected to return to the occupied West Bank until June.
Jenin residents sceptical
In Jenin, many residents told Al Jazeera they were had little faith in the Israeli offer.
One man, a taxi driver, said Israel was not interested in security. "Even if they brought thousands of Palestinian soldiers ... Israel would sabotage every initiative," he said.
The Jennin forces, the Jerusalem Post reported, would maintain order during the day, while the Israeli army would continue to patrol during the night.
Israel maintains that the offer will help the peace efforts by strengthening Mahmoud Abbas, the Palestinian president, in facing rival faction Hamas.
But Palestinian officials say the Israeli moves are not enough. Abbas told reporters in the West Bank town of Ramallah:
"There are many obstacles. Our hope is that these obstacles will be removed." He said that he remained committed to the goal of reaching a peace deal by the end of the year.
On Monday, Barak rejected a key Palestinian demand, saying Israel would not remove any of the hundreds of West Bank checkpoints.
The Palestinians and many officials around the world including Tony Blair, now a Middle East envoy, have said the travel restrictions are stifling the West Bank economy.
Israel says the measures are needed to prevent attacks.
Across Gaza and the West Bank on Wednesday, three rallies took place, with demonstrators calling for Palestinians to stop fighting and unite.