His call came during his talks with his visiting Chinese counterpart Xi Jinping at Bangabhaban on Friday evening.
After the meeting, Press Secretary to the President Md Joynal Abedin told reporters that Hamid had requested Xi to 'allow all Bangladeshi products duty-free and quota-free entry into the Chinese market to reduce the current trade deficit'.
Stating that Bangladesh was an important South Asian country, the Chinese president said the two countries have had diplomatic ties for 41 years and bilateral relations were strengthening more and more.
Xi said there was scope to diversify bilateral ties in different areas, including trade and agriculture.
He pledged that China would continue its cooperation as a development partner of Bangladesh, Abedin told reporters.
Mentioning his meeting with Prime Minister Sheikh Hasina earlier in the day, the Chinese president said they had decided to work together and take up a master plan to boost bilateral relations.
Foreign Minister AH Mahmood Ali, State Minister for Foreign Affairs Shahriar Alam, Foreign Secretary Shahidul Haque and other top officials were present during President's Hamid's meeting with Xi Jinping.
After the talks, President Xi attended a banquet hosted by President Hamid in his honour at Bangabhaban. Prime Minister Sheikh Hasina joined the two presidents along with others.
Xi, the first Chinese head of state visiting Bangladesh in three decades, arrived in Dhaka on Friday morning on a two-day visit. President Hamid received him at Shahjalal International Airport.
Later in the afternoon, Xi and Hasina held a bilateral meeting at the Prime Minister's Office.
Afterwards, in their presence, the officials of both countries signed 27 deals on cooperation in a number of sectors, among which are coastal disaster management and construction of a Karnaphuli tunnel.
The deals altogether relate to 15 agreements and MoUs and 12 loan and mutual agreements.
Xi and Hasina also unveiled the plaques of six projects at the ceremony.
The 13-member delegation that Xi is heading has several key ministers besides leaders of the ruling Communist Party of China.
On Saturday morning, the Chinese president will lay floral wreaths at the National Memorial in Savar before departing for India.