The order said the two leaders who made objectionable comments while campaigning during election rallies be removed from the list of BJP's "star campaigners".
Thakur and Verma can still canvass for the BJP but they will have to bear the campaign expenditures.
A political party bears the expenses of canvassing by star campaigners. But the candidate has to show expenses of organising meetings and rallies by other campaigners in his/her election expenditure accounts.
While political parties have no limit on the amount they can spend for electioneering, candidates can spend a maximum of Rs 28 lakh for campaigning in Delhi assembly polls.
"The Election Commission has ordered the removal of Anurag Thakur and Parvesh Sahib Singh Verma from the list of star campaigners of the Bharatiya Janata Party for the general elections to the Legislative Assembly of the NCT of Delhi with immediate effect and until further orders," an EC press note stated.
Responding to a question during a Cabinet briefing here on the EC order, Union minister Prakash Javadekar said, "I have just got information that EC has issued some direction. We will study and if necessary, present a letter and application."
He also said if something wrong has been uttered, the BJP will take cognisance as it is a thinking party. "I will speak only after examining the order."
"But more importantly, the BJP is putting up a balanced campaign with positivity. We are discussing about the development of Delhi.What we will do for Delhi what the Modi government has done for Delhi and the way the state government created hurdles in our efforts) ... this is our mainstay. Development is the focus of the speeches made by main speakers," he said.
During an election rally here, Thakur, who is a Union minister, egged on the crowd to raise an incendiary slogan -- "shoot the traitors" -- after he lashed out at anti-CAA protesters. He was issued a show cause notice on Tuesday.
West Delhi MP Verma on Tuesday said what happened in Kashmir with Kashmiri Pandits could happen in Delhi, warning that lakhs of anti-CAA protesters in Shaheen Bagh could enter homes to kill and rape women.
Verma was issued a notice by the EC for his remarks on Wednesday.