"Hamas's step is a positive indication if they really dissolved the administrative committee and showed its willingness to hand over control to the unity government", Mahmoud al-Aloul, Abbas's deputy in the Fatah party that governs the West Bank, said on Voice of Palestine radio.
Egypt has been brokering talks with Abbas's Fatah group to implement a deal signed in 2011 in Cairo with Islamist Hamas to end its dispute and form an interim government before elections.
Hamas said in a statement on Sunday that it has dissolved its shadow government, that it will allow the reconciliation government to operate in Gaza and that it agrees to hold elections and enter talks with Fatah. All efforts to reconcile two rival groups and to form a national unity government have failed until now.
Israel and Egypt have since imposed a blockade on Gaza; Egypt intermittently opens its border crossing into Gaza.
The Palestinian militant group Hamas says it is aiming for talks with rivals Fatah as it aims to end their decade-long feud. The UN has even ruled that enclave, one of most densely populated areas in world (2 million inhabitants) would become "unlivable" by 2020.
Last Tuesday, Fatah Central Committee Member Azzam al-Ahmad, who is now leading the Fatah delegation in Cairo, said if Hamas disbands its administrative committee, Abbas would lift its punitive measures against it.
Punishing measures included reducing electricity payments for the Gaza strip and cutting salaries for civil servants there.
Hamas agreed to dissolve the administrative committee it had formed in March previous year to run the daily affairs in the Gaza Strip, the coastal enclave that Hamas has been ruling since it had violently taken control of it in the summer of 2007.
However, Bjorn was skeptical if Hamas's announcement on Sunday would lead to a full-fledged reconciliation between Hamas and Fatah.
This means that electricity has often been provided for less than four hours a day, and never more than six.
The deal was not clear whether Hamas is ready to place its security forces under Abbas' control - a key sticking point that has scuttled past attempts.
United Nations officials have urged Israel to lift its decade-long blockade of Gaza.
Trade of accusations and disagreements went deeper between the two sides, until Hamas formed the committee to run Gaza and accused the consensus government and Abbas of turning their backs on the Gaza Strip.