challenge

2.[~ sb to sth] to invite sb to enter a competition, fight, etc.;
    to suggest strongly that sb should do sth (especially when you think that they might be unwilling to do it)

• Mike challenged me to a game of chess.  
• The opposition leader challenged the prime minister to call an election. 

.... 다음영어사전(OALD)

4. VERB

If you challenge ideas or people, you question their truth, value, or authority.

• Democratic leaders have challenged the president to sign the bill.     
• The move was immediately challenged by two of the republics.     
• I challenged him on the hypocrisy of his political attitudes.

5. VERB

If you challenge someone, you invite them to fight or compete with you in some way.

• A mum slashed a neighbour's car tyre and challenged her to a fight after their daughters fell out.     
• He left a note at the scene of the crime, challenging detectives to catch him.     
• We challenged a team who called themselves `College Athletes'.

... Cobuild