Baroness Warsi was cleared of any serious breach of the ministerial code over an official trip to Pakistan.
But Conservative Party chairman Baroness Warsi said the strike action across the UK was "going to benefit no-one".
BBC: Public sector strikes: MoD picket outside Donnington base
Conservative Party co-chairman Baroness Warsi denied the Conservatives had deliberately fought a lacklustre campaign to benefit their coalition partners.
But Conservative Party co-chairman Baroness Warsi said the previous Labour government's Future Jobs Fund had "squandered millions" on short-term placements.
Conservative party chairman Baroness Warsi has said she wants to keep her job, amid speculation that she may be replaced.
But in 2008 Baroness Warsi wrote an article in the Guardian promising to make khat an illegal drug if the Conservatives came into power.
Baroness Warsi's two-day delegation of seven British ministers to the Holy See will include an audience with Pope Benedict XVI, who visited the UK in 2010.
The latest debate on faith in Britain was ignited after Conservative co-chairwoman Baroness Warsi warned that the nation was under threat from a rising tide of "militant secularisation".
As well as Justice Secretary Jack Straw, the other Question Time panellists are expected to include Conservative peer Baroness Warsi, Lib Dem home affairs spokesman Chris Huhne and playwright and critic Bonnie Greer.
He defended the decision not to refer Mr Hunt, but to refer Conservative Party co-chairman Baroness Warsi, saying the Leveson Inquiry into media standards was already looking into issues of Mr Hunt's conduct.
On Thursday shadow community cohesion minister, Baroness Warsi, who appeared on Question Time for the Conservatives, said it was a "real shame" Mr Woolas was not on the programme to defend his comments.
There's a little more committee activity on Thursday: the International Development Committee (at 9am) takes evidence on violence against women and girls, with Foreign Office Minister Baroness Warsi, and International Development Minister Lynn Featherstone.
Tory spokesman for social cohesion, Baroness Sayeeda Warsi, believes that advice and education about khat is simply not enough to tackle the problem.
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