Mr Swire added that "the past can not be addressed by focusing solely on one case".
Dr Jim Swire, who lost his daughter in the bombing, has also supported that move.
Dr Jim Swire, who lost his daughter in the bombing, will also sign the petition.
Swire's operations span a number of different industries, from aviation to beverages to trading.
Dr Jim Swire, who lost his daughter Flora, believes that Megrahi was wrongly convicted.
Mr Swire - a doctor - felt forced to stand down as a partner in his medical practice.
The British conglomerate Swire Pacific is the majority shareholder of Cathay with a 41.97% ownership stake in the airline.
In response, Northern Ireland Office minister Hugo Swire said the government had previously expressed sympathy to the Ballymurphy families.
Mr Swire said that, if Libya really was turning its back on terrorism, his group supported Mr Blair's efforts.
This trade was very profitable for a handful of Scottish-run trading houses with names like Jardine Matheson and Butterfield Swire.
Dr Jim Swire, of the UK Lockerbie Families group, criticised the Tory leader, Michael Howard, for saying that the visit would distress relatives.
BBC: Kathleen Flynn accuses Blair of "short-term memory loss"
Dr Jim Swire, a spokesman for the UK Families Flight 103 Group, kept details of the meeting which he attended closely under wraps.
The British conglomerate said it was considering a separate listing of Swire Properties Ltd. on the main board of the Hong Kong stock exchange.
The minister was accompanied by Nigel Dodds MP and Northern Ireland Minister of State, Hugo Swire for the meeting with Andrew Robathan in London on 4 July.
Swire's property portfolio is heavily weighted towards office and retail space in some of the city's prime locations on Hong Kong Island, including Pacific Place and Taikoo Place.
In the latest sign of bullish sentiments about Hong Kong's real estate market, Swire Pacific said on Tuesday that it was looking to spin off its property division.
Controlled by the founding Swire family, the company's operations also include property development in Hong Kong, marketing and distribution of Coca Cola products in China and supplying offshore oil rigs.
Meanwhile, it has emerged that Foreign Office minister Hugo Swire told MPs in December of "illegitimate efforts to interfere with shipping and tourism in the region" by "elements in Argentina".
BBC: Falklands row: Sun places advert in Argentina newspaper
The band of last year's event might not have the subtlety of the Prodigy or Chase And Status but they do have one trick (Rob Swire's synth) which works superbly well.
Conservative shadow culture spokesman Hugo Swire added that the deal was a "huge defeat" for Ms Jowell, adding she had led the BBC to believe it would get a generous settlement.
Northern Ireland minister Hugo Swire said the government would ensure that the difficulties were "cleared up and cleared up quickly, so that people can go about their normal business in Northern Ireland".
BBC: Ulster Bank IT problems 'horrendous', says NI secretary
Swire did not provide a possible time frame or any financial details for the listing of its real estate unit, but analysts estimate it could come in the first half of next year.
"Workers with little to no experience are overlooked in China, but we find they're like sponges, absorbing quickly and willingly, " says Anthony Ross, general manager of The Opposite House, Swire's boutique hotel in Beijing.
Swire also hosts beauty classes, helping new female workers like 22-year-old Wan Xu, who recently graduated from hospitality school in China's central Hubei province, learn how to use make up and fix their hair.
Hugo Swire, Shadow Secretary of State for Culture Media and Sport, said the government's gambling reforms were supposed to tackle problem gambling and organised crime, but in fact were likely to make it worse.
But Mr Swire said it would have been a good idea if Mr Howard had talked to the families before making his comments and that as far he knew he had made no effort to do so.
BBC: Kathleen Flynn accuses Blair of "short-term memory loss"
Yet some of the deals in which British groups such as Swire and Hongkong Telecom, which is owned by Britain's Cable and Wireless, have sold stakes to Chinese groups look more like the results of greenmail than the formation of useful partnerships.
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