The announcement is a part of the proposed Cotton Purchase Agreement for which the two countries have exchanged the final draft.
Besides, both the sides signed a textiles sector collaboration agreement aimed at strengthening the economic ties between the two nations.
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Cotton season runs between October and September.
"Under the proposed Cotton Purchase Agreement, in 2013-14 I have assured Bangladesh Textiles Minister Abdul Latif Siddique that Bangladesh textiles mills will get smooth flow of cotton and would have no difficulties in sourcing it from India, even if we have to ban cotton exports to other countries," Textiles Minister K Sambasiva Rao said.
He was talking to reporters after meeting Siddique here.
"As regards the agreement, the final drafts have been exchanged between the three sides -- the Textiles Ministry, Cotton Corporation of India (CCI) and Trading Corporation of Bangladesh (TCB)," Rao said.
Under the draft pact, private sectors of two countries and CCI under the Textiles Ministry (India) and TCB under the Bangladesh Ministry of Commerce will engage in exports and imports of cotton.
"In case of imposition of restriction on export of cotton by India at any time, the CCI and TCB of Bangladesh will determine through consultation the remaining volume of cotton exports in the season," a Textiles Ministry official said.
At present, export of cotton is in the Open General Licence (OGL) category with registration of export contracts by the Directorate General of Foreign Trade (DGFT).
India's cotton exports are estimated at about 100 lakh bales in the current cotton season. In the previous season, the country exported 129 lakh bales of cotton.
As regards the textiles sector collaboration pact, it has come into effect from today and shall remain in the force for a period of five years, the official said, adding that the agreement will be reviewed on completion of every two years.
"We have signed the textiles sector collaboration agreement which would act as a major trade facilitation mechanism, by establishing institutional mechanism for collaboration through Joint Working Group (JSG)," Rao said.
Under the pact, India and Bangladesh would cooperate in different areas like fashion technology through exchange programmes, skill exchange through institutions and upgradation and enhancement of productivity, efficiency, management techniques and R&D.
The pact was signed between Textiles Secretary Zohra Chatterjee and Bangladesh Textiles Secretary Ashraful Moqbul.
"We respect each other's sentiments, we understand each others needs and we want to go parallel and we wish that Bangladesh growth is also substantial which is also good for the India," Rao said.
Also, the two sides discussed about establishment of a successor organisation for the International Jute Study Group in Dhaka through joint efforts at the UNCTAD.
India and Bangladesh together account for nearly 94% of the world's production of jute and allied fibre.
During Prime Minister Manmohan Singh visit to Dhaka in September 2011, he announced duty-free import of 61 items from Bangladesh that were barred from entering India.
A majority of these items 46 to be precise, relate to textiles, particularly garments.
Subsequent to the Prime Minister's visit, India has further brought down duties on most imports from Bangladesh under the South Asian Free Trade Agreement (SAFTA) agreement.