Coalition Senators unsuccessfully sought to block extending the time for the Senate Select Committee for the National Broadband Network (NBN) to report back to Parliament, in a move aimed at bringing MPs from the House of Representatives back into the hearing room, and break former Communications Minister Stephen Conroy's dominance over the committee.

The Senate Select Committee was established last year following the election of the Coalition government to replace the Joint Parliamentary Committee that had been led by former Independent MP Rob Oakeshott. There are three Labor senators, three Coalition senators, and one Greens senator on the committee, meaning the government is in the minority on the committee.

At the time, the government claimed that Shadow Communications Minister Jason Clare had been "rolled" by committee chair Kate Lundy and Conroy in setting up the committee, but Greens communications spokesperson Scott Ludlam said at the time that at no time did Communications Minister Malcolm Turnbull seek to re-establish the joint committee.

In its short life span, the committee has held eight hearings, with NBN Co executives and chairman Ziggy Switkowski hauled before the committee to face a grilling from Conroy on the changes to the project since the election of the new government.

The executives have complained that appearing at the committee has taken a significant amount of time away from running the company.

In its interim report , the Labor-Greens majority recommended that NBN Co completely redo its strategic review amid claims that the review had "lowballed" its June premises passed target, and had failed to take into account a number of cost savings NBN Co had developed prior to the election to bring down the cost of rolling out fibre-to-the-premises.

In the Coalition minority response, and the official response from Turnbull, the majority report was labelled "grossly misleading" and "self-serving", aimed at protecting Conroy's legacy. Despite the strong criticism Turnbull indicated that the government "looks forward to continuing the public hearings" of the committee.

However, yesterday when Lundy moved to extend the life of the committee for the remainder of the first term of the Coalition government, Coalition senators voted against it. The motion was upheld, however, with 37 senators voting for the extension, and 29 voting against it.

A spokesperson for Turnbull said that when the new Senate begins sitting in July, the government may seek to re-establish the joint parliamentary committee that would include both House of Representative MPs and senators. It is unclear what the make up of the committee would be, but the move would be aimed at bringing Clare and fellow Labor communications spokesperson Michelle Rowland into the committee, and reducing Conroy's influence.

As ministers, neither Turnbull or Parliamentary Secretary for Communications Paul Fletcher would be on the committee if it was re-established.

A spokesperson for Lundy's office had been approached for comment.