Without taking Kejriwal's name directly, Anna said, "...if anyone feels there are shortcomings in the bill after it is passed, they should fast for it."
"I have read the provisions of the bill properly. If you (Kejriwal) think the bill has any shortcomings, fast for it," Anna, whose fast for passage of Jan Lokpal Bill entered the sixth day today, said while talking to reporters in his village Ralegan Siddhi.
The anti-graft crusader said several of his expectations from the legislation have been met and he expressed satisfaction over the bill which has been presented in the Rajya Sabha.
Read current Lokpal Bill properly: Kiran Bedi to Arvind Kejriwal
"Three issues for which we had campaigned in the past, including Citizen's Charter, are also being addressed," he said.
Asked about the differences between him and Mr Kejriwal, Anna said, "I don't wish to comment...Why should we quarrel?"
"The government's control over CBI has been removed in this bill. I saw 13 such points and told the government that I welcome this," Anna said.
"That is why I thought that the bill is beneficial to the people and country," he added.
"I told the government that I am thankful for tabling the bill in Rajya Sabha. Bring it in both the Houses in this session itself. If needed, extend the tenure of Parliament," he said.
"However, I am confident that this need may not arise as people are saying that the bill would be the first thing to be taken up in Rajya Sabha tomorrow," he said.
Thanking major political parties, including the Congress and the BJP, for supporting the bill, Anna said, a few are not supporting it. "So, if there is a ruckus while passage of the bill, pass the bill amid ruckus but pass it anyhow," he said.
"There are still five days left for the session to end. If you desire so, it can be brought in both the Houses during this period. If there is paucity of time, extend it by a few days," he said.
"I won't end fast till the bill is passed. I want to live for the country and fight for the country, for society. I have to take up issues like right to reject and right to recall," he said.
Anna has been fasting outside Yadavbaba Temple in his village since December 10.
His associate Kiran Bedi said, "If some people are saying that the current Lokpal bill is weak, they haven't read it properly. They must read it."
As per the bill provisions, if any matter is given to CBI, the government will not interfere, she said.
"Kejriwal should reread the bill," the former IPS officer said.
"Tomorrow, I will be in Delhi, watching Rajya Sabha proceedings and inform Anna about the goings on there," she said.
"Those who are calling the bill Jokepal have not read and understood it. They should go through the draft and then jump to conclusions," she said.
(With PTI inputs)