The Treasury said it expects about one million savers to purchase the bonds, which will be on sale until 15 May.
Chancellor George Osborne announced the move yesterday as officials reported £7.5 billion worth has been sold so far, with over 610,000 savers purchasing bonds since their launch in January.
On the first day they were launched the NS&I website crashed and the phone lines struggled to cope with the demand, leading to predictions they would sell out within days.
The government expects that the total issuance could be around £15 billion, after originally allocating £10 billion for the bonds.
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There is an annual interest rate of 4% for the 3 year bonds and 2.8% for the 1 year bonds and an investment limit of £10,000 per bond per person.
Chancellor George Osborne said: "Our 65 plus pensioner bonds have been a huge success, and are already helping hundreds of thousands of older savers who have done the right thing, by boosting the return on their savings and securing a more comfortable financial future.
"I want to ensure as many older savers as possible can take advantage of these market-leading bonds, which is why I'm confirming today that potential savers will have months to invest in these hugely popular products, if they wish.
"It's part of our long term economic plan to support savers and boost hardworking peoples' financial security at all stages of life."