Demur (day-mur)
(verb) to raise questions, or object; to linger.
(noun) the act of making an objection; an objection raised.
Examples:
1. While many board members were ready to build the new park, June demurred because she thought the site was too close to the highway.
2. When Ward invited June inside, she demurred on the front porch a little longer.
3. June’s demur led many to question the location of the new park.
4. June didn’t mind if Ward was disappointed by her demur to his invitation inside.