WINDSOR, ENGLAND - Indian President Pratibha Patil received a red-carpet welcome from Queen Elizabeth II on Tuesday at the start of a three-day state visit to former colonial power Britain.

The queen hosted a banquet for Patil, the first Indian woman to be elected to the ceremonial role, after she was taken in a state carriage procession to Windsor Castle, where she will stay during the trip.

The queen paid tribute at the dinner to the strong, historic ties between the two countries and the contribution of India's population in Britain.

"Britain and India have a long shared history which today is a source of great strength in building a new partnership fit for this new century," she said in a speech to guests who included Prime Minister Gordon Brown, Harry Potter author JK Rowling and leading members of Britain's Indian community.

The British monarch also remembered the Mumbai terrorist attacks that killed 166 people and injured more than 300 others last November.

"I would like to pay tribute to the courage and steadfastness shown by the Indian security forces and the people in the face of this great tragedy."

Patil, the first Indian head of state to visit Britain for almost 20 years, praised the shared values of their two countries. She also invited the queen to visit New Delhi for the 2010 Commonwealth Games.

"Your Majesty, the ties between India and the UK are built upon shared values and traditions. There are numerous commonalities between our two countries," Patil said.

"We are vibrant democracies with a free press and active civil societies, we both believe in freedom, dignity and respect."

Improving trade links and boosting British investment in India will be high on the agenda for the visit, which will include talks with Prime Minister Brown on Wednesday, Indian officials said.

Britain is the biggest European investor in India and bilateral trade between the two countries was worth 12.6 billion pounds ($28.7billion) in 2008, according to the Foreign Office in London.

The countries also cooperate closely on counter-terrorism, in particular sharing information on attacks on transport systems in London in 2005 and Mumbai, as well as climate change and non-proliferation.

Some 1.3 million Indians live in Britain, representing about two percent of the population, according to Foreign Office figures.

Patil, who arrived on Monday, will also join the queen on Thursday in launching the baton relay for the Commonwealth Games in New Delhi.

The relay will start at Buckingham Palace in London and travel through 70 countries before reaching the Indian capital when the games open on October 3 next year.

Patil will also visit Cyprus before returning home on Saturday.