The federal government has dismissed a proposal to add new parliamentary oversight of Canada's foreign-focused spy agency at a time when Ottawa is boosting counterterrorism powers in the aftermath of two attacks last week.

The rejection comes three days after the government tabled its own bill, C-44, to boost the powers of the country's other major intelligence agency, the Canadian Security Intelligence Service (CSIS), which has a domestic focus. The federal government also continues to review what other new counterterrorism powers it will add in the aftermath of attacks last week that killed two soldiers, though sources said Thursday those changes are still under discussion and not "imminent."

Bill C-622, known as the CSEC Accountability and Transparency Act, was tabled in June by Liberal MP Joyce Murray and calls for more oversight of the Communications Security Establishment Canada (CSEC), the country's foreign-focused electronic spy agency. The bill would, among other things, create a parliamentary committee to oversee national security operations, including CSEC. Currently, it's overseen by a commissioner.

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Ms. Murray held a briefing on the bill Thursday along with Jean-Jacques Blais – a former Liberal MP, minister of defence and member of the Security Intelligence Review Committee (SIRC) that oversees CSIS – and Wesley Wark, a professor who studies national security issues. Both praised the bill, with Prof. Wark in particular stressing the bill would not diminish CSEC's powers.

Oversight by a committee of MPs and senators is "about making sure that our intelligence and security agencies have the tools and the funds they need to protect Canadians and to protect Canadians' rights," Ms. Murray argued in Question Period.

However, the government was cool to the proposal. Public Safety Minister Steven Blaney said "robust oversight exists," though he cited SIRC, which oversees CSIS, not CSEC. Nonetheless, during debate on Bill C-622 Thursday evening, Conservative MP Roxanne James called the bill "needless and duplicative in nature" and said the government would not support it.

After last week's attacks, "we will not overreact, Mr. Speaker, but at the same time as legislators we must not underreact to the threats that are upon us," Ms. James told the House of Commons during debate over the bill.

Since last week's attacks, Canada's law-enforcement agencies have said they're reviewing their approach. A 30-year-old gun collector originally from Pakistan was arrested this week on immigration charges, under allegations he poses a threat to Canada. Immigration Minister Chris Alexander distanced himself from the arrest Thursday, saying only "those are law enforcement issues."

However, it is the Immigration and Refugee Board that is presiding over the case and charges relate to his immigration status.

On Monday, Mr. Blaney tabled C-44. One of its provisions boosts CSIS's power to operate internationally – putting it alongside CSEC. Mr. Blaney has declined several interview requests from The Globe to discuss the bill.

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His department, along with that of Justice Minister Peter MacKay, continue to review what new powers should be added beyond Bill C-44. The government has been said to be considering whether to give police new powers for "preventative arrests," whether to reduce the threshold of how much evidence is needed to limit or monitor a suspect, and whether to criminalize online statements that support terror groups. Asked Thursday whether preventative arrest – without a charge – is still on the table, Mr. MacKay said only "we have elements of that now."

Prime Minister Stephen Harper has said a review of what new counterterrorism powers are needed will be "expedited" after the attacks. It continues to be a priority, one government source said Thursday. "There is a need to do this on an expedited basis, but nothing is imminent," the source said.