LONDON (AFP) - Prime Minister Gordon Brown welcomed Indian President Pratibha Patil to Britain Wednesday on the second day of her state visit which he said showed growing ties between the two nations.

The pair held talks at Brown's Downing Street office as Patil made the first visit to Britain by an Indian head of state for almost 20 years, discussing a range of issues from business to terrorism, officials said.

"I welcome the president of India to Britain on her state visit. This is a sign of the strategic partnership that is growing between India and the United Kingdom," Brown said before their talks.

He highlighted the cultural ties between the countries, noting more than one million people travel between India and Britain each year, about 1.5 million people of Indian origin live here and about 30,000 Indian students study here.

"Relations will grow stronger as we develop closer educational, cultural and economic links between these two great countries," the prime minister told lawmakers in the House of Commons.

Downing Street said the two leaders -- who last met during Brown's visit to India in January 2008 -- discussed business investment, education, climate change, terrorism and global poverty during their meeting.

Patil, the first Indian woman to be elected to the ceremonial role, received a red-carpet welcome from Queen Elizabeth II on Tuesday which included a banquet in her honour at the monarch's Windsor Castle residence west of London.

The queen paid tribute to the strong historic ties between India and its former colonial power, and the contribution of ethnic Indians 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 at the dinner.

The 148 guests included Brown, senior royals, "Harry Potter" author J. K. Rowling and leading members of Britain's Indian community.

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

Patil, who was staying at Windsor during her three-day trip, highlighted the shared values of the two countries and praised the multicultural diversity of London.

She also invited Queen Elizabeth to visit New Delhi next October when the Indian capital hosts the Commonwealth Games.

The two women will launch a baton relay for the Games on Thursday at Buckingham Palace. The baton will travel through 70 countries before reaching New Delhi for the start of the games on October 3 next year.

"Your majesty, the ties between India and the United Kingdom are built upon shared values and traditions," 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 are high on the agenda for the visit, Indian officials have said.

Britain is the biggest European investor in India and trade between the two countries was worth 12.6 billion pounds (20.7 billion dollars, 13.9 billion euros) in 2008, according to the Foreign Office in London.

Patil's visit included a trip to the Natural History Museum and the Indian high commission on Wednesday, where she was to receive a collection of letters by Mahatma Gandhi on behalf of the republic.

The president was also due to meet Indian business leaders before joining a reception hosted by heir to the throne Prince Charles and a banquet laid on by the lord mayor of the City, London's financial district.

Patil will also visit Cyprus before returning home on Saturday.