Ijaz said the demands were made months before Chaudhry's dismissal, whose sacking by Pervez Musharraf, the Pakistani president, set off a national political crisis.
The statement was one of three filed in the Supreme Court by officials who were present when Musharraf sacked Chaudhry on March 9.
The statements filed on Thursday are the government's response to Chaudhry's claim that he was intimidated by Musharraf and military generals who wanted him to resign, but that he refused.
Ijaz, whose organisation is one of Pakistan's three main spy agencies, said that Chaudhry asked him to come for a meeting a few months ago at which he started discussing the internal political situation.
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"It would be in the best interests of Pakistan for Musharraf to step down"
Jim ibarra, Cyberjaya, Malaysia
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"He was of the view that the president should dissolve the assemblies as they were becoming a nuisance and hold elections under the CJP [Chief Justice of Pakistan]," Ijaz said in the affidavit.
In Pakistan the president must dissolve parliament and the senate before calling elections, which are held under an interim administration.
"He wanted me to assure all concerned that he will make things very smooth," once he was put in power, Ijaz said.
He said Chaudhry "used to task him on a regular basis to provide information on judges in Punjab [province] so he could build a database for his own reference".
Lieutenant General Hamid Javed, Musharraf's chief of staff, and retired Brigadier Ijaz Shah, the intelligence bureau director, also filed statements on Thursday.
Political crisis
Chaudhry's suspension has sparked the biggest political crisis since Musharraf seized power in a bloodless coup in 1999, as well as political violence that has left 40 people dead.
Opposition leaders say Musharraf ousted the independent-minded judge to remove legal hurdles to his bid to remain army chief past the end of 2007, when he is constitutionally obliged to quit the post.
Presidential and parliamentary elections are also expected late this year.
Chaudhry is appealing against his suspension over allegations of nepotism and misconduct, which he denies.
Chaudhry on May 29 filed an affidavit saying that he was not allowed to leave Musharraf's army house for six hours on March 9 and that he was virtually kept under house arrest till March 13.
The judge said military intelligence chief Ijaz confronted him after he refused to step down and told him: "This is a bad day, now you are taking a separate way."
Ijaz denied this. "Nothing discourteous was said by anyone during these discussions... No demands were made," he said in his statement.