The three ministers could also discuss the role of Pakistan in stabilising the region, Indian official and analysts said.
"All three have shared concerns about the violence emanating from Afghanistan, but there is divergence between India and China on the Pakistan military's role," said Uday Bhaskar, a New Delhi-based strategic affairs analyst.
"India would like to see what stand China takes on Pakistan."
India is locked with Pakistan in a struggle for strategic influence over Afghanistan. New Delhi sees Beijing as backing Islamabad with deep ties to the Pakistani military.
New Delhi is seeding Afghanistan with development projects worth $1.2 billion but its citizens and embassy in Kabul have come under repeated attacks from Islamist militants uneasy with Hindu-majority India's growing clout.
Many in India see the hand of Pakistan's military in these attacks. Islamabad considers Afghanistan a fall-back position in the event of war with India.
"China will seek to balance its pro-Pakistan tilt with its concerns about Islamist radicalism spilling on to Xinjiang province among the Uighurs," said an India government official.
Along with Tibet, Xinjiang is one of the most restive and politically sensitive regions in China. Uighurs are Muslims native to Xinjiang, which Islamists call East Turkistan, and have cultural ties to Turkic peoples in Central Asia.
Bhaskar said while Islamist violence in Afghanistan was not an immediate problem for Russia, it was wary of religious radicalism overhauling Central Asian countries and reaching its borders.
The three sides could also discuss their response to climate change negotiations in Copenhagen in December. The three countries are among the top polluters in the world.
INDIA-CHINA TENSIONS
Focus also remains on a bilateral meeting between the Indian and Chinese ministers to try to scale down differences over their disputed border and unequal trade that have flared in recent months and sparked fears the rivalry could spin out of control.
Officials said the two ministers could discuss tensions arising from troop mobilisation along their border and the visit of Tibetan spiritual leader the Dalai Lama to a disputed Indian state Beijing claims as its own territory.
But progress could be limited with the two leaders striving only to mute the strong rhetoric after the Indian and Chinese prime ministers met in Thailand at the weekend.
"This meeting provides an opportunity to improve the atmosphere, lower the harsh rhetoric that has reached unprecedented levels," Brahma Chellaney of the Centre for Policy Research said.
The two sides have an experts forum which has held 13 rounds of border negotiations but little progress has been achieved. The two sides fought a brief war in 1962 over their border disputes.
Bilateral relations have warmed in recent years, mostly on the back of mutual trade expected to pass $60 billion next year, a 30-fold increase since 2000. The two sides are also coordinating positions on climate change and global trade.
But friction over a lingering dispute along their Himalayan border has been rising, most recently over plans for Tibet's spiritual leader the Dalai Lama to visit the Indian border state of Arunachal Pradesh in two weeks.
India has been home to the Dalai Lama since he fled a failed Tibetan uprising against Chinese rule in 1959.
The two sides have also clashed over bilateral trade -- heavily tilted in favour of China -- visa policies for their citizens and resource rivalry in Asia and Africa. India has dozens of cases against China at the WTO.
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